I have covered in the past, and I have also not covered. It really does "depend". It "depends" upon where you live and if you plan on using your camper over the winter months or not.
We covered our PUP and our first TT. We used he TT at home in the winter, so kept one panel accessible for the door and left it so we could raise one side to run the furnace. It was a pain in the neck.
Second camper (longer and a new cover), we tried to do the same thing. Bigger pain in the neck to use it in the winter having to manipulate the cover. Then noticed after about the 3 or 4th year (2nd trailer), the paint was wearing where the cover rubbed. So quit using the cover the cover from that point on (we had the camper 8 years).
Last and current camper we are not covering. Found out by experience from the previous camper, that if you want to use the camper, and there is snow on the roof, on top of the camper, and then you make plans to go somewhere or use it, you've got a real headache attempting to get that cover off with a foot of snow and ice on top of it.
So current trailer, no cover. We plan a couple winter trips to Florida every year now (1 week in December, and 1 week in March). The last thing I want to deal with is getting a cover off the roof when a foot of snow is on top of that.
So really, it does "depend" on how you plan on using your camper over the winter. If you are storing completely, 100% and locking down till spring, covering is a good thing. If you plan on using the camper in the winter and (especially) if you live in the snow belt, you'll be very frustrated with a cover.
If you live in the non-snow states, you may want to cover if you have to park under trees or areas where sand storms could damage the exterior. In those cases, covering is a good choice.
So once, again ... it does "depend". Determine how much you will use the camper if you do cover, what are the weather conditions where you live, and that will help you decide.
For what it's worth, there is a good way to put the cover on and take it off, but there is no "easy" way to do it. You still have to climb on top of the camper and man-handle the cover. No way around that unless you have someone else do it.
Previous camper: No cover year:
Previous camper: Cover year, after moving to our current house:
Current camper, no cover: