An Unusual Slav Gambit

How about this in the Caro Kann (can't find it anywhere via Google searches):
1. e4 c6 2. d4 d5 3. e4 dxe4 4. f3
Diemer-Duhm type idea in the Caro instead of the French.
Illustrative game: https://www.chess.com/blog/neilparker62/left-right-ko-combo
The problem is that a lot of slow systems, like the Colle System, and aggressive gambit lines, like the Diemer-Duhm gambit (which isn't sound to begin with), are dependent upon Black impeding his own development somehow. For example, in the Colle System, 1.d4 d5 2.Nf3 Nf6 3.e3, White can answer 3...e6 (blocking in his own Bishop) with 4.Bd3, 5.c3, 6.Nbd2, etc. However, against 3...Bf5 or 3...Bg4 requires faster action from White. For example, 3...Bg4 4.Bd3 is not good at all for White, he is virutally forced into playing 4.c4, contesting the Queenside, now that the Bishop has left the Queenside.
The problem with the Blackmar-Diemer Gambit is the same thing, Black has not committed to shutting in either of his Bishops.
And that is the problem with your line. Neither Black Bishop is blocked, and so Black has free development and is up a pawn. Normally the downfall to the Caro-Kann is that it takes Black 2 moves instead of 1 to break in the center with ...c5, while the French sees the Bishop blocked by his own pawn, but can hit White's center quicker. So for an opening where Black is slow, why give away pawns? Why not get the extra piece developed while Black is slow to hit White's center?
4.f3? in the Caro-Kann makes zero sense.
If they play Bf5 instead of Kc6 you can go e3 and then you have the idea g4-Bg6 and then h4 (look for a game played by Morozevich with White). This idea is actually good and you can play it without worries.