You can install anything up to 2" bolt on. Some require removing parts of the bumper plastic and then reinstall it after the hitch. The total load rating of a v is about 950 pounds which includes passengers. Toyota does not recommend towing due to the suspension, rear hub bearings and brakes. I used one for things like bike carriers but others have pulled trailers. I know the rear hubs can't take much load but wear generally results in howling rather than hubs getting loose. A heavy load will also force more regen, lower mpg and could aggravate an already fragile gen3 engine. Going down long mountain grades could be a problem as increased regen would fill the hv battery and switch to engine and friction braking alone. So if the loads will be light you may be ok.
In my gen 2 I hauled 2600 lbs of gravel over hilly roads, when I moved from state to state 8 years ago I hauled 2000 lbs 700 miles, both with a 600 lbs single axle aluminum utility trailer. Twice I've towed 2800 lb 280ZX's with a tow bar over 100 miles. pic related is a load of wood from Home Depot to build a storage shed Breaking The Prius Towing Convention | PriusChat
IMHO; you can do anything you want - It's a free country. The real question is should you. If you get into an accident and/or injure someone; you're going to have to explain the extra load and the other sides attorney will probably note that Toyota does not recommend towing. I've seen idiots rig up leaf-spring U-bolt clamps to mount a 2" hitch onto uni-body cars. Wouldn't want to be near them on a highway. Just my two cents....
If you are going to tow never exceed about 80% of the cars weight. You always need some tongue weight but you can have too much, and never load more weight at the back of the trailer. Also reduce your speed, there's a reason some states have a lower speed limit for towing.
I tow all the time w gen 3's. 5x8 open trailers, 4x8 enclosed, a 19ft skiff, and a 23ft Bay boat. The latter creates too much wind drag. I max at 55mph w that and the heat generated w my foot pinned to the floor is more than I should subject it to. I can hold my foot to the floor for 15min at higher speeds w the open trailer or smaller boat but higher speeds offer more cooling. At 55mph I don't get enough air for the mg1 mg2 and computer to keep that up for long. Like boating, and electrical, the 80% rule for constant load is an max recommendation. It's. A good guide
Yes you can. I installed the Draw-Tite 24967 Class 1 Trailer Hitch, 1-1/4-Inch Receiver and it worked just fine for a lot of trips towing a 4x8 harbor freight folding trailer. I have never overloaded the trailer though as the maximum I ever pulled was ~800lbs. The Prius v did not feel any different pulling that load. The install is easy as etrailer,com has a full install video with the Prius v and this exact receiver. Also great for the hitch mount cargo carriers. Earlier this year I switched to the EcoHitch Hidden Trailer Hitch Receiver - Custom Fit - Class III - 2" Part Number: 306-X7192. A bit more complicated of an install but again there is video and it went smoothly. A 1 1/4" receiver is probably all you need, but I upgraded to a 2" receiver for a few reasons. 1st) I wanted a larger tongue weight for loading up cargo carriers and also sometimes I step on the hitch with a trailer attached and I am 200lbs by myself(I know the 1 1/4" 200lb tongue weight has safety margins built in for the forces encountered while underway). 2nd) The variety of 2" receiver aftermarket accessories dwarfs that of the 1 1/4".(far more light weight aluminum cargo carriers in 2" than 1 1/4"). 3rd) The larger receiver resists the torsion on cargo carriers from unbalanced loads better than the 1 1/4". 4th) cause I wanted to. Either way, do it.