I have bitten into many shot when eating game birds, everything from no. 9 up to no. 4. I've never seen a one that was misshapen enough to mention, much less mushroomed, or even flattened. And I used to load a lot of chilled (soft) shot years ago
for doves and quail. Not even pure soft buckshot flattens any at all unless it hits large bone.

IMO, the harder the shot is the better it kills, not because the individual shot are more potent, but because they will pattern better and put more of them in the bird.

SRH.

May God bless America and those who defend her.