Not all horses prefer riding backwards.
I think those that do is because they expect to be getting out thru the back, not because they balance any better than riding forward.
Yes, I read the long ago study in Australia that had determined thru blood work that horses hauled better, less stressed riding backwards.
Maybe some do, or maybe the stress was from other than which way they faced?
Practically all ranch horses that spend hours a day being hauled from place to place, loaded and unloaded, not tied in there, singly or several of them, seem to chose to ride slanted with front to the left, butt to the right.
That is probably because highways are crowned and the middle is higher than the sides and maybe why so many choose to ride a bit on a slant to take advantage of that to compensate with the vagaries of accelerating and stop/go driving is for them.
Two of our horses, going to move fresh cattle to water, just jumped in there, not tied, will back out on command, settled themselves like most ranch horses do, preferably over the axle/s, looking ahead, at that described slant.
They do it every day, several times a day, could move up to the front, or turn around and ride any other way they choose, but this way is their choice, that of most ranch horses in those ranch stock trailers: