World champs wouldn't have been a lot different other than it would end earlier. If you lose a game, you need to win a game to be even. That doesn't change even if you make it 100 points for a win.
It would impact multi person events more, but not incredibly. I think some interesting options are things like .7 for draw and 1.2 for win as black. Other options are to make 3 move repetitions illegal (now they're a kind of zugzwang). Last option that I like would be to add a time penalty for drawing in future matches. I think chess needs to become less even, and you could do that in interesting ways if you were willing to mess with the time (or even who moves first) in future matches. Incentives to win now (vs maybe win later) should reward aggressive play early in tournaments and make players who are falling behind more incentivized to fight mid tourney.
I imagine if a draw was counted as a loss to both sides, there would be a lot more aggressive plays, since just stonewalling a skilled opponent would be the same as losing.
Machines don't have any concept of a tournament. Humans go into drawn lines and get rid of tension in order to play the tournament meta-game. Since draws are worth so much, it's often a good idea to just bail out with a draw.
A lot of human positions wouldn't be drawn by machines, they would keep hammering the opponent.
If you could agree to a draw in tennis, you would see a lot of draws where players want to save their energy and don't think this match counts that much.
In other sports players don't play for draws. In chess, because draws are worth so much, some players will try to draw with black and win with white. If chess were more combative players would intentionally stay away from drawish lines.
Many ways to change the game have been put forward before. Including banning draws in positions that are not known to be draws from a table base, changing how many points you get for a draw (you could get less than 1/2), forbidding early draws, changing what happens if a tournament is drawn.
These kinds of rule changes make a big difference. Like, 3 points for a win, 1 point for a draw. Now, you can't comfortably sit as black and bank a lot of draws because you won't be able to as easily catch up.
Rules for draws in tournaments are really absurd these days. A drawn classical tournament or even the world championship gets decided by rapid games. What's the point in playing classical if you win by playing rapid? The world championship is particularly problematic in this regard.