Such a system would not be possible because there would be countless extra factors to consider... Alas, it is only possible to give a rough value of the pieces (the values you describe), but it is up to the player to decide on their pieces value at any given moment .
Points system


Could we post ideas on our own points systems, maybe with positions?
An idea would be to start with the reference point that at the start of the game, the queen at home is worth 100 points.

I'm only speaking for myself... but...
The idea of counting points in the middle of a game seems like a waste of resources.
I am typically much more concerned about positions, tactics, and strategy during a game... and use points to justify trades.

I think Nytik is rigth: it´s posible to give a rough value to each piece (i think that´s the way computers works), but a chess match is an open system, because your oponent´s style it´s also an extra factor. That was the reason why deep blue suspiciously played french defense against Kasparov (he didn´t like this openning).
Talking about inside factors, a lot of them can be included trying to evaluate a position (see the chess.com computer, he gives you a relative score in each position) but i think that´s a very very complex work. One proof is that computer´s rating decrease when they play without his book opennings (fortunately, if not chess study would be near to finish).
In my opinion, the only thing a human can do is what diskamyl says: have some own generalities that gives extra points to your pieces (passed pawns, center pawns, atacking pieces,...) or lower points (two pawns in same column, closed bishops...). Do the same thing to your oponnent pieces and you will have a relative score of the match.
Concluding, i think it could be interesting to make an specific simple method, particularly for beginners or intermediate players. The way? dificult work; masters or computers should give us the guidelines.

It's about Space...
The assigned value of a given piece arises from its ability to control space. Indeed, the whole of chess depends upon what is meant by controlling the space about the opponent's king. Control all of it whilst attacking and it is checkmate. Control all of it - where the opponent's king and any of their other pieces on the board have no place to move - and it is called stalemate. Most often, but not always (can you say "sacrifice"), winning an opponent's piece translates directly into additional space controlled by the taker. It is often heard in analysis that an exchange was bad for white because he gave up a good knight for a bad bishop. What is meant is that the bishop that was taken in exchange for the knight was a bishop on a color that was largely occupied by the player's own or by the opponent's pieces, thus having very little ability to exhert control over diagonals of its color. The same thinking dictates that a piece in the center of the board has ostensibly greater power because at the center, all other pieces removed, all pieces have more places to which they might move, then when positioned on say the 4th or 5th rank in the "a" or "h" file. Again, this points to the ability of a piece, a combination of pieces or indeed, a position to "master" space. I think of the point value of a piece as little more than a quantification of the inate power of a piece, independent of its position, and independent of the other pieces on the board. At any given point, one should focus on the value of a piece arising only from its current or projected control of space, and specifically, the space around the opposing king. I don't think this analysis suffers at all from my lack of rating points. Rather, those who intuitively or through study understand best how to use pieces in combination to control or gain control of space will win.
Leading on from the "what is it worth?" topic:
Everything has a value in chess - the system everyone knows is the "1 point for a pawn, 3 for a bishop etc."
Does a system exist which gives everything a value, depending on it's position, what it is attacking etc.? For example, a knight is worth 10 points on the 3rd rank, 11 on the 4th, 12 on the 5th. A bishop is worth 10 points, but a bishop pair in an open game is 25 points.
I'd be grateful if you can point me in the direction of the right book/write one for me.