How different would chess be if a stalemate was a win? Historically stalemate has been handled in different ways. I wonder how different chess would be if it was a win for the stalemating player.

Has enough thought been put into this so that it's possible to give a clear answer? Would there be significantly less draws and more wins for white? More aggressive play? Would changes be seen already in the opening?

A related question that already has been asked is why the actual rule is as it is. The accepted answer to that question talks mostly about history and the logic that has been given for the rule, but another answer goes into how endgame would be different with this variant instead. There it is a side issue for explaining something else, which has made someone suggest this is a duplicate question. I hope that the actual what-if question can get more thorough answers for itself than when it is a side issue of a related question. For example my issue about if changes would be seen already in the opening have not been brought up.

The ideal answer for me would be if something like AlphaZero (without preconceived notions) had spent some time playing this variant, but I guess I'm out of luck on that?
Building on SmallChess' answer, KP vs K endgames that are normally drawn would be lost. This has very big ramifications, as there are many rook endgames where the side up a pawn can easily transpose into a (formerly drawn) KP vs K endgame. For example:


The Philidor Endgame
A normal K+R+3P vs K+R+2P on the same side of the board.
A K+R+4P vs K+R+3P where the extra pawn is a passed a-pawn. If the defending rook is behind the pawn, the endgame is considered barely drawn. However, the attacking rook might be able to exchange the extra a-pawn for a pawn on the kingside, reaching the aforementioend K+R+3P vs K+R+2P endgame.


This logic can also be applied to other endgames, such as K+Q+P vs K+Q. However, Rook endgames are the most common, and by making stalement = a win, many of these fundamental endgames are ruined.

Once that has happened, it's often not difficult for the better side to transpose down into one of them (especially the Philidor).

So making Stalement a win would drastically lower the number of draws that happen when one side is defending an endgame. However, there are many cases where no one was ever winning in an endgame (i.e., even material throughout), and most of these would probably result in draws still. The reason is that many draws in equal endgames arise from an "impasse" both sides create, where neither can make progress.