I havent seen that exchange or done that exchange since about a million years ago. It was popular "back in the day" when we all thought it was a good exchange on f2/f7.
Rook and pawn for two minor pieces

Your observation matches Yusupov who counts a rook as 4.5, pawn as 1 and minor pieces as 3.
So in order for this to work, you generally need to get fairly immediate compensation in the form of a strong attack, etc.
His way of counting also makes sense in terms of sacking the exchange. You often get a pawn with the minor piece, so you are "only" down .5 pawn. That can be worth it depending on the compensation, strong attack, blunt an attack, etc.

Your observation matches Yusupov who counts a rook as 4.5, pawn as 1 and minor pieces as 3.
So in order for this to work, you generally need to get fairly immediate compensation in the form of a strong attack, etc.
His way of counting also makes sense in terms of sacking the exchange. You often get a pawn with the minor piece, so you are "only" down .5 pawn. That can be worth it depending on the compensation, strong attack, blunt an attack, etc.
Yes, depends a lot from the compensation.
There's a Karpov game where he makes that exchange, IIRC - I'll try to find it later.
Generally, the closer you are to an endgame, the more valuable the R+P are.

I think I've heard many times that it's a bad trade for the minor pieces. The knight and the bishop is far stronger pieces than a lazy rook in the opening. Those minor pieces is so often "the creative" pieces in the middlegame too. In a endgame I would have choosen the rook.

How about a Bishop and 5 pawns vs a rook and 3 pawns. Which would u take? I had the bishop and extra pawns and was offered a draw. I accepted.

Here's a game in which I lose a rook and 1 pawn in exchange for a knight and bishop. In that position, I was happy with the trade but it's hard to say if it had a real effect on the outcome, as games at my level can be won and lost from anywhere at any time. The exchange starts on move 10.

Your observation matches Yusupov who counts a rook as 4.5, pawn as 1 and minor pieces as 3.
So in order for this to work, you generally need to get fairly immediate compensation in the form of a strong attack, etc.
His way of counting also makes sense in terms of sacking the exchange. You often get a pawn with the minor piece, so you are "only" down .5 pawn. That can be worth it depending on the compensation, strong attack, blunt an attack, etc.
2 coordinated rooks are better than a queen
Yusupov mentions this. He also mentions that 3 minors are generally stronger than a Queen.
Any counting method is necessarily imprecise and will involve exceptions, and judgements about whether you have adequate compensation.
For example some methods consider Bishops as slightly better than Knights. Others recognize that much of the difference is actually down to the strength of bishop-pairs and give a bonus of about .5 pawns specifically for that, etc.
One of the many things that separates the people who can really play this game from the patzer is their ability to better evaluate positions. It is trivial to show positions where normal methods of counting lead to very poor evaluations of the position.

Strong players do not spend more than seconds to sac material for positional advantages. Weak players would not do this because they don't know much about strategy. I remember saving already two games with material down because I prepared well before exchanging stuff.

Your observation matches Yusupov who counts a rook as 4.5, pawn as 1 and minor pieces as 3.
So in order for this to work, you generally need to get fairly immediate compensation in the form of a strong attack, etc.
His way of counting also makes sense in terms of sacking the exchange. You often get a pawn with the minor piece, so you are "only" down .5 pawn. That can be worth it depending on the compensation, strong attack, blunt an attack, etc.
2 coordinated rooks are better than a queen
Yusupov mentions this. He also mentions that 3 minors are generally stronger than a Queen.
Any counting method is necessarily imprecise and will involve exceptions, and judgements about whether you have adequate compensation.
For example some methods consider Bishops as slightly better than Knights. Others recognize that much of the difference is actually down to the strength of bishop-pairs and give a bonus of about .5 pawns specifically for that, etc.
One of the many things that separates the people who can really play this game from the patzer is their ability to better evaluate positions. It is trivial to show positions where normal methods of counting lead to very poor evaluations of the position.
The knight also gain value if you have a queen
I heard/read this somewhere too. But, I don't know 'why horse gains value if minister is present'? Do you know?

Coming to the topic of the thread: when to sac an exchange?
1) sac an exchange to remove a key defender during an attack.
2) sac an exchange to remove a key attacker during defence
3) minor pieces(specially bishop pair) are more useful in opening and middle stages, so don't trade them for a rook/elephant.
4) in endgames, rook pair is more useful.
5) sac an exchange to get to a winning king & pawn end game.
6) during middle game, sac an exchange to remove the monster horse of opponent sitting on your third rank and creating problems of coordination of pieces.
7) sac an exchange to promote your pawn.

Ashvapathi: The knight and queen happen to coordinate extremely well with each other. They make an often deadly combo.

Ashvapathi: The knight and queen happen to coordinate extremely well with each other. They make an often deadly combo.
Yeah, but that is true for all the pieces. What is so special about this particular combo?
Mikhail Tal has a game, against Johannessen I believe, where he sacrificed/exchanged two minor pieces for a rook and pawn. It was exactly the kind of trade we've all learned not to do! But there were special features of the position that made it an attractive idea. GM Serper wrote a couple of articles about this subject
https://www.chess.com/article/view/a-rook-or-two-minor-pieces
https://www.chess.com/article/view/a-rook-or-two-minor-pieces-part-two

Ashvapathi: The knight often coordinates better with the queen than a bishop would because:
1) The knight can jump over obstacles
2) The knight can attack without being attacked
3) The bishop can't cover both color squares.
These two pieces just happen to coordinate very very well together.

Here's a game in which I lose a rook and 1 pawn in exchange for a knight and bishop. In that position, I was happy with the trade but it's hard to say if it had a real effect on the outcome, as games at my level can be won and lost from anywhere at any time. The exchange starts on move 10.
The thing is, in that game you had an extra rook, but that rook wasn't active, both rooks were very passive. When there is an inequality you have to use it.

Here's a game in which I lose a rook and 1 pawn in exchange for a knight and bishop. In that position, I was happy with the trade but it's hard to say if it had a real effect on the outcome, as games at my level can be won and lost from anywhere at any time. The exchange starts on move 10.
The thing is, in that game you had an extra rook, but that rook wasn't active, both rooks were very passive. When there is an inequality you have to use it.
I actually play white in that game, with the extra minor pieces. You make a good point, my opponent failed to adapt to the circumstances and his rooks were passive, whereas my minor pieces all contributed fairly significantly. This comes from the exchange occurring early in the game, when my minor pieces were already active and his rooks had yet to move (aside from castling) and were subsequently unable to.
Most of us know that you will usually not get two minor pieces for a rook and a pawn. At least I know this from the opening theory. The points are equal, but two minor pieces counted more than a rook and a pawn. Two pawns would be probably okay, but not just one.
Did you have already games where it was good to exchange for example a bishop and a knight for a rook and a single pawn? I don't mean which something drastic happening afterwards, like mate or winning more material. Just curious.