You will probably find you get as many answers here as you have found on (the rest of) the Internet.

That said, my own approach is that if there is not a reason to take something down, leave it up. Reasons to take something down would include: (A) ugliness (there are few that fit into this category for me, I like the different elevations and textures as the season develops, and some things (e.g., ornamental grasses) are positively lovely); (B) disease/pests (though I personally don't subscribe much to this one, especially since along with overwintering pests will be overwintering beneficials); and (C) unwanted seeding.

Many of your identified plants are rampant self seeders but the "damage" is already most done for them (e.g., get ready for LOTS of brunnera, plenty of pulmonaria, a bunch of new Echinacea/Rudbeckia and lots of Monarda!). But again, this is not a bad thing depending on your goals. New plants, free, are not a bad thing and you can also weed out or pot up and give away unwanted plants. And while they may not be true to their parents they might be even better, and lots of plants have a habit of popping up in just the right place.

In case you haven't noticed, I am in favour of not doing much in the winter by way of clean-up. But I have done it both ways (sometimes with a lawn mower!).

The answers to your question will be as varied as there are gardeners. Every one of us has our own ways and reasons for doing things.

I like simican don't do much to prepare for winter. If I have tall plants--Which I don't have many, because the wind knocks them over and I lose the blossoms. I cut them down by half. I pull up the annuals but I leave them laying in the beds. Most of the other perennials I leave to cut down in the spring.

The reason I do this is so the plants sticking up will catch the snow so they have good cover. Snow helps protect the roots. I've lost more plants to no snow cover and cold temps. in spring and fall than I ever lost to a very cold winter.

If I have a tender plant or one I'm pushing the zones for I tend to mulch it well and again the snow cover helps.

That's my practice and reasons. Others will say they like neat beds for the winter and they cut everything down. I imagine you will have a few years of trial and error before you hit on your way to do it.

When I empty the pots of flowers I put them over my roses, dirt side down.; and put leaves from the yard on top of that. I used to go out and buy dirt to put on them then got this idea, it seems to really protect them or anything else I want to protect from the winter. I also put any other plants on top depending how tall the roses are. Tricia

My rule of thumb is, if it is obviously brown and dead and quite done for the year, OK to cut it back. However, I've grown more into leaving some things up for winter interest. I'm going to try leaving my sedum heads up this year. I have them next to an ornamental grass, and I think that will be a nice winter look.

Then there are a few things that may be not quite hardy in this zone, or susceptible to moisture getting in the crown and succumbing to that (I've heard this is why a lot of garden mums don't make it). I have Agastache that I will leave up. I may leave the Black and Blue Salvia up too.

Some things that are late to emerge, like Balloon Flower, you can cut them back to about 6" stubs so you will know where they are next year and not plant over them.

So, I guess it's really kind of individual, based on the plant and your preference for tidiness.

Of the ones you mentioned, I might leave the coreopsis up (if it's a threadleaf, like Moonbeam). Some people leave Echinacea seed heads for the birds, but they do reseed like crazy. Bee Balm...I've never had it before this year, but I think I'll cut mine back. I think the Dead Nettle will just die back on its own if I remember correctly - I had it years ago. Ajuga doesn't need cutting back ever, unless you want to shear it after bloom.

I take down peonies for the disease mentioned above. But I read somewhere that irises, for example, get through the winter better if you leave the foliage so I am going to try that this year.

I am not one who cares about winter interest all that much but I leave butterfly bush and russian sage all winter and cut them down pretty low in early spring.

two thoughts ....

1) you do what you can get done in fall.. and do the rest in spring ...

or 2) ... the best advice.. presuming you have more than one of each .... do one .. and leave the other.. experiment ... i have learned more by experimenting.. then i ever did from a book or the web ... one of the reasons that there are so many different opinions.. is because everyone has her own little micro-climate.. about which our advice may or may not work ....

what might be more important .. depending on where you are [you dont say] .... is whether or not a nest of mulch might not help your plants through the winter ...

in reliable snow cover... most things survive.. since the plants are out of winter wind and winter sun ...

if there is no snow cover... warm days in the dead of winter can lead to ground thaw .. which can hurt some perennials ...

i think that is much more important than whether you cut them back ... you may be putting the horse before the cart, as they say ...

ken

some have suggested.. that the natural dried canopy .... is the plants own little mulch system.. to protect the crown for winter .... reducing direct winds.. and direct sunlight on the crown itself ...

ya know.. most plants have been around for millions of years [perhaps not in the cultivar form we see now].. and cope just perfectly ... but for us coming along.. and being a bit retentive about having a 'clean' garden for winter ...

IMHO .. there are only two reasons IT 'HAS TO' be done ... e.g. hosta and slugs... and ... voles or rodent problems ... both vermin populations can be reduced by taking away where they hide/eat all winter ...

otherwise.. its your personal preference ...

ken