I haul long distances and I have personal experience with horses who have developed respiratory issues due to not being able to get their head down below their knees from time to time. Of course one would argue to just tie them longer but if the rope is tied long enough so that they can get their heads down, then the rope gets under a front leg and then they are caught and depending on the horse you have - well then it depends on the accident that happens afterward - hence - I don't tie.
I haul in halters with the rope attached thrown over their back loose - been doing it for over 20 years - in stock trailers and slants with dividers. Worst thing that happens is the rope slides off and gets peed on - no big deal. My horses can back out AND turn around and walk out forward - been in an incident where the trailer was stuck and the back end was high in the air - too high to back out so I turned them around and they were able to leap out forward. Much safer.
Took a technical large animal rescue course this year - one of the things the firefighters/rescue workers/sheriffs/ etc complained about most was horses who have been tied in trailers took too long to get out - often the animals were upside down and twisted, caught by the rope holding them in - they said that so much time was wasted trying to reach in to a mangled trailer and cut the rope (usually with a knife on a long pole b/c getting in there with the animal was NOT safe) and most horses go into shock way before they could even get the rope cut. Horses who were loose tied were immediately assessed and often easier to handle and move b/c they weren't stuck on a twisted rope - and because they were untied, could often right themselves or at least sit up.
The emergency rescue folks have seen many instances where a trailer gets in a wreck and they see snapped/twisted necks, pulled/ripped/torn muscles - in most cases the animal who was tied ended up being the animal that was mangled the most because the body (as gruesome as it sounds) was not allowed to roll with the trailers momentum. Animals who aren't tied had a better chance coming out with only scrapes and bruises while tied horses often ended up going to the vet a week later after the incident with serious issues liked cracked C1 or C2, and on a regular basis, ended up dying a few days later. Emergency folks I have personally talked to at this course (who actually spoke at the course) and those here where I live vote for untied as well when it comes to horses.
The horse has a better chance of survival if it can move with the trailer - even if that means doing complete cartwheels over and over. Locking any one part of their body down and then rolling them over and over is a death sentence.
I had already been trailering without tying for over two decades before I took that course - it only confirmed it for me. If a technical large animal rescue class comes to town, I would recommend you take it - even if you aren't working as a type of rescue personnel - it is an eye opener for the average horse owner on so many subjects - tying in trailers was just one of many.
Clippityclop is finally getting to spend some time in the saddle!