well I bet this gets a lot of opinions LOL
yrs back when they used to MAKE a TRUCK a TRUCK< and had heavy duty parts on things like tailgates, I'd of said NO< don't worry about things
but these flimsy tailgates we have now, and the fact the WHOLE tailgate is thin sheet metal and made as cheap as possible(yet costs crazy amounts for a new one LOL)
I'd be a little worried about hauling a ATV far sitting on the tailgate, all the more so if on very rough roads!
adding some 2x10 sounds like a great idea to me, , but they might be a problem to carry when you want the tailgate UP, as you will need them to be about 7 ft long I bet?
another idea might be a good HD sheet of treated plywood, throw in when hauling, take out when not needed!
another thing you can maybe do is find a good cable shop and have some MUCH stronger cables made up, that you know will handle some weight
won't really help if tailgate itself bends though LOL
the tailgate on my 2006 dodge 3/4 ton was maybe 50 lbs, the one on my 2016 I think is about 20 IF that, couldn;'t believe how cheesy they made it??
also don't forget that its NOT just hauling the atv on the tailgate you have to worry here, BUT when driving UP and into the truck, your placing a LOT of load on them cables
so again, having better cables made up, would be money well spent IMO!