The question is do you want to have the shortest expected number of turns until you win, or a 100% win rate. Playing safe (min-max) is what ensures the 100% win rate, but you might be making games longer on average.
Mini-max isn't even 'playing safe'.
Consider the following choice of moves, each leading to one of 5 random tile inserts:
Move A, which leads to 5 possible moves with the following game state goodnesses: ['Loss','Win','Win','Win','Win']
Move B, resulting in: ['99%CertainLoss','99%CertainLoss','99%CertainLoss','99%CertainLoss','99%CertainLoss']
Minimax is never going to choose A. Is that really what you want, even if your strategy is 'play it safe'?
Also, we should note that the "value" in "expected value" doesn't have to mean "score." It could be the logarithm of your score, or your chance of winning against a rational adversary, or even the enjoyability of the game to spectators (if you have a precise metric for that).