it would change the mindset of players ... so for keepers not to palm a ball round the post like they would usually do, or someone shooting from distance just to try and get a corner, or a player not going for a tackle
Giving the opponent a corner is generally worth avoiding, regardless of a tie-breaker tally. Likewise playing to gain a corner is already a common tactic, either for its own sake (i.e. to cross the ball into the box for a scoring chance), or to kill time at the end of a game. These are already parts of football strategy.
However your point is correct, and teams could play just to boost the corner tally, for example, if a team gets a first corner, it could just repeatedly take short-corners and hold the ball in the corner area to attempt to gain a succession of corners, rather than make any attempt to work the ball towards the goal-mouth. With good practice, this could be the football equivalent of nursery cannons in billiards, a tactic which made an already extremly dull game infinitely duller.
Anyway, the influence of the impending tie-breaker upon the preceding
play is already common, e.g. teams playing very defensively in
extra-time and/or timewasting to get to the shootout is currently a
I am not exactly in favour of using corners, but it is better than something like "shots on target" or "possession" which would more strongly influence the preceding playing style. If the objective is just to separate the two teams, tossing a coin is fine with me.