Question

Can other common plants grow in areas where lots of insectivorous plants grow

Answer 1

I think, no. where insectivorous plants grow the other plants don't germinate

Answer 2

Usually no.

First of all lack of insects in that area lacks the chance of pollen exchanges by insects hence chance of new tree growth becomes limited.

In general the areas where insectivorous plants grow the soil in general lacks nitrogen, which plants fix from the insects’ body.

Other plans have to depend nitrogen from soil which they can’t get.