Why would a crack in my pool pump strainer basket cause it to pull air?

It shouldn’t. You could actually be able to run it without the basket

Last one I had would create a cyclone effect if the strainer wasn’t in and would pull air very quickly.

A crack in the strainer basket won't make your pump pull air. The issue is probably the same thing that caused the basket to crack.

In the fall when we swim less, if at all, we tend to not dump leaves out of the strainer basket often enough. When the basket gets full of leaves it becomes a partial plug on the skimmer. The increased pull pressure from the pump partially blocked by the leaves is likely what cracked the skimmer basket. Also, when it gets that full of leaves, air gets pulled through gaps in the leaves into the return line, causing your pump to pull air. Keep the basket clean and none of this happens.

Mine has a drain plug on the bottom that the O-ring was cracked causing it to suck a little air. Maybe check that too?