Some perennials like hosta can bull their way up through anything practically. Daylilies can as well but if it’s too heavy a layer they will suffer. Most others will just smother.
If a perennial has a hard time getting to the surface and uses up more energy than what is typically used, it might not have enough energy to produce a flower, all you’ll have is a bed of green leaves.
But if you do know where everything is, mulch away; just leave “mulch-free” zones around each known perennial site.
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