A groomed garden appeals to some, but some of us like a more natural look.
Seed pods forming are part of that natural look.
The seed pods give a hint of what next year's garden will be like.

I like to have areas for both styles, but more often than not I'll end up planting something that I should leave for the birds in my groomed beds anyway.

I deadhead throughout spring and summer mostly in hopes of more blooms, but toward the end of summer I let things GO.

A natural look is nice in the right application, but even then, if some kinds of plants are not deadheaded, they will not keep blooming. So deadheading prolongs the bloom season and then allowing them to set seed later in the year is nice to look at and great for the birds in the winter.

I like to leave those seedheads for the birds to enjoy. I actually leave those kinds of things till spring. Yes, the clump might look nicer after the head heading but I do go ior the more naturalized look. I want my garden to be very friendly to the backyard songbirds as I really enjoy having them around.

I let plants develop seeds. For example, I love Black Eyes Susan seed heads. I leave them on the plants till spring. They add character to the winter look. I deadhead only roses, but only till late August or September; after that, I let them set rosehips. Particularly, I like clematis seedheads.

On the other hand, deadheading makes sense in formal gardens.

Working for a landscaping company, I find that more of our customers prefer to have the perennials deheaded to keep the garden looking tidy. For them. it's all about curb appeal.

Partly depends on the plant, of course. Black eyed Susan may not have been the example some of us would choose, given wanting the seeds for birds or self sowing. Or collecting.
But peonies for example, those are a good one to deadhead and trim back the tips.
Petunias and pansies too, we probably aren't looking for persistent seed heads, but for long blooming.