This is what the skeppists did
Even though I have kept bees for over 50 years and have more than enough colonies to make any increase I need, I am still willing and happy to collect and hive stray swarms. My reasons are perhaps different than others, but despite my advancing years, I'm still fit enough to climb ladders, trees and buildings. I have collected many hundreds of swarms and I still find some of them a challenge and even as an old hand I am always learning more.
I like to collect swarms as a service to the public. If I know a beekeeper who would like a swarm, I'm happy for them to have any swarm I collect, but I would prefer it if they came along and took it themselves, with me helping if they need it.
I think all beekeepers, however many colonies they have, will find the hiving of swarms a useful way of making increase. Providing the usual precautions are taken when hiving them, to reduce the chances of infection with foul brood, there shouldn't be anything to worry about. I find the vast majority need requeening, as they are worse bees than my own. I have spent a long time improving mine and it is very rare that a stray swarm is as good as my own.
As an experienced beekeeper, I am on the local and national swarm lists. I'm also well known locally as a beekeeper, so I get a lot of swarm calls during a normal summer. I'm not greedy and I would prefer beekeepers who have a greater need for a swarm than me to have them. What often happens is that some beekeepers who have lost bees during the winter go on the swarm list, then when they have enough, don't want any more. This often means there are a good number available that nobody wants.
If you only want a small number it is quite easy to deal with, but if you wanted more I suggest a "holding apiary" where all your swarms go. This will help in the unlikely event of you getting foul brood.
I disagree with the view that swarms aren't worth collecting. I can be as little as 15 minutes taking some swarms, yet considerably more on others. If I take more than an hour I consider it to be difficult. Even if you double that time and you get a decent swarm, it has been worth it, especially if you can get your expenses paid.
If the swarm is reasonably early, a reasonable size and the foraging good, you may be able to build the new colony up so it doesn't need winter feeding. If you treat it for varroa as soon as you get it, hive it as advised, then it should go into the winter as a strong, healthy colony that doesn't need feeding.
Taking, hiving and managing swarms is a useful way to teach beekeepers and it will give the increase that many BKAs need.