Are all Pawns equally valuable?

Recently I've been thinking as to why certain pieces move the way they do. I have some ideas as to how certain aspects of the games rules came to fruition. I wasn't intending to improve my Chess game through this thought experiment but it has definitely changed the way I see the game, play the game.

Now I find the pawns more valuable as the game goes on. I don't think it's any secret that position is everything in the game of Chess, as having more pieces than your opponent means nothing if you can't escape a forced mate. So Pawns, from their initial position before move 1, what do you believe to hold true. Are all Pawns equal? Or does the file in which they march forward on hold more value than other files?

One thing to keep in mind is that Pawns can change files through capturing pieces. But the "a" Pawn will most likely never get to the "h" file in a high level game. Another thing to note, the "c" Pawn and the "f" Pawn are positioned symmetrically from one another and look to be the same, but we know that isn't the case. Like the "d" and "e" Pawn, they start on opposite colored squares and when pushed they open up activity for different pieces and or open up squares for ones King to be checked on.

Checking isn't the same as when another pieces is attacked. If your Queen was attacked and you could move her, the choice is left to you. While a check is a forced move that's limited to a specific set of lines. Because of this, I'd assume like most do, that the "f" Pawn is the least valuable. I also believe the "c" Pawn to be more valuable than the "b" and "g" Pawn, Possibly even the "d" and or "e" Pawn. The "a" and "h" Pawn have a lot of late game potential so I'm not sure where to place their value, but I'm leaning towards believing that the "h" Pawn in most games to be more favorable of the two.