A "thru-axle" could be a problem as there may be nothing to hook onto on the left side, unless spreading the dropouts and squeezing the mount under the dropout. This isn't the same as a quick release.
As @
fietsbob mentioned, so far I've done well with a skewer mounted trailer. Make sure you're using quality steel skewers. I usually mount the skewer lever to the right side on the rear.
Your rear axle is the strongest part of the bike. Think of it, it is where all the pulling of the wheel goes to.
Some chainstay/seatstay mounted trailers have issues with disc brakes, and perhaps large rear hubs. But, the axle mount should be fine in most situations.
Our local bike co-op likes the seat post mounted trailers, and they'll take heavy loads.
https://eugene.craigslist.org/bik/d/...708094543.html
I don't think I've ever pulled one of them, but one advantage is that the trailers are easy to move around the shop by hand. Less of a trip hazard? They also have an integral kickstand at front of the trailer which is down all the time.
@
fietsbob also mentioned Bike Friday. If using a BF trailer, they use an male end of an air hose either permanently welded or bolted to the chainstay, and a piece of air hose and the female hose coupler attached to the trailer to give the trailer hitch flex. It works quite nice.