Annual cover crops in perennial beds

Does it make sense to plant annual cover crops in a perennial bed or will they compete?

Let us put on our suppose cap and see if some situations would make sense.
Suppose you have a perennial bed that has heavy leaf cover in the summer so not much tries to grow under the plants until the leaves fall and the rains come then undesirable weeds come up.  If you seeded a desirable cover crop too cover the soil and feed the soil organisms during the dormant period then the perennial plants would benefit the next growing season.
Suppose you have a perennial bed like speargrass where you want to be able to find the spears in the spring but weeds will hide them and hoeing the weeds could damage the crowns.  A selective cover crop that covers the soil under the fronds of the speargrass during the summer and leaves a mulch during the winter would be highly beneficial.
So put on your suppose cap and sit by your perennial bed and let the ideas fow.

What's growing in your perennial bed?

I plant N fixing cover crops all the time in and around my fruit trees, moringa, chaya and other perennial plants.  If the space is going to be bare for more than a month or two, I'll plant something in that space to make sure the soil microbes are being fed with root exudates and that we are generating additional bio-mass on the surface as well as below the soil line (with the root mass).

Go for it.

The ytube site "I am organic gardening" has several videos on using cover crops.  In one he shows the effect of a) his cover crop of rye + clover all around the tree on 4 peach trees, and b) just letting the natural weeds grow up around his trees on 2 peach trees.  The ones with the cover crop had twice the top growth and a few first year peaches.