I've been growing Organically for the last 51 years, so I'm a bit different in some way's.
I remove living plant tissue only when there is rot or damage. I use supports for any plant that needs help.
It goes against everything I have observed, that modifying the shape & growth of a living awake plant can have
many positive effects on the health of the plant. I have had plants die from pruning, most likely I introduced a disease
when I cut them.
We really enjoy seeing the different natural shapes our plants grow into, when left to their own design. Just my .02
If you are trying to overwinter or otherwise grow a pepper indoors, or within confined space parameters, there are significant advantages to pruning, topping, and shaping them. Like
@Indiana_Jesse already said, it will cost you in production.
Given the short seasons in the North, I wouldn't dream of topping or pruning anything non-ornamental, unless I were planning to overwinter and grow it on as a Bonchi or otherwise.. But there are certainly benefits to doing it, depending on the culture you are employing and desired results.
If pruning is killing your plants, it is likely as you suspected, or just ill timed.. Or your experience could be different in the South. How much pruning have you done on them? I usually keep some isopropyl alcohol around to disinfect tools between plants/cuts depending on the scenario.
I haven't been pruning Capsicum long, wanting to grow and learn the different natural habits first.. But I haven't seen anything to suggest pruning is a poor cultural practice with them, and quite the contrary. That is, outside of reducing your potential harvest that season. It also sets any harvesting back a solid month in the north here, but that might be desirable.
Bird Aji for example.. Single season topped vs. untopped. Everyone shown in Trade #2 Nursery.
Same untopped post-harvest, then topped.
And who says LemonDrop has to be a gangly plant? For me the choice is having one plant, or 4-5 dwarfed ones in the same amount of space. Not every Capsicum lends itself to pruning, but most seem to do just fine, from what I've seen. Most of the early season toppings were a happy accident this year.. But I'd do it again.
I've got plenty of other examples, but you could find even better material by looking at posts by Bonchi artists who have been doing this a while. Here's one of my 2nd Seasons From last years overwinter..
It was late getting out, and only set about half the pods it could have, yet comparable to single season harvests I've had.. Given the cultural issues and weather this year. For a small container, I was pretty happy, and still harvesting them indoors.
All of this with the knowledge that my plants are probably poor examples of what they could be, and others have in similar containers.
Pruning can be done with natural or contrived forms in mind, but that has little to do with whether the cultural practice itself is organic. There are many instances where pruning can improve the health and longevity of plants, and allowing it to grow unchecked can result in reduction of the same.. Capsicum not excluded(especially culturing indoors). A great many crown type shrubs and woody plants can choke themselves out in time, and naturally die off years before they would if they were pruned.
Also, there are many forms of pruning that take place as a result of natural processes too, so to think of it as unnatural is a bit off. Weather, rabbits, and birds are the three most common for me.