An engine that's always working at near it's maximum capacity will fail long before an engine that's working at a quarter of it's capacity. Most people wouldn't dream of constantly running their engine bouncing off the red line of rev limiter. The same applies to towing; if you frequently tow large, heavy loads (for instance, earth moving equipment), you want to get a vehicle that's rated for much higher tonnage than the weight you'll regularly be towing. Given that campers are usually very light weight (but only slightly more aerodynamic than a brick), you can get away with towing on in a car infrequently. You should probably not do it daily.
You may also find that it's less fuel efficient to tow a heavy load in a small-ish car than the same load in a light truck.
(BTW - I'm generally opposed to taking vacations in this way. I prefer my vacations on a motorcycle, or on foot with a backpack. I'm not currently in the kind of shape I would need to be in in order to do bicycle camping.)
Edit: I don't have a truck. It's cheaper for me to rent one on the rare occasions that I need one than it is to buy one and deal with the associated costs of owenership. That said, the Home Depot rental trucks suck, because they're solely RWD, and they have no grip on my road unless there's a literal ton of weight in the back.
Nobody complains about big cars whilst they're towing, and if they were doing it everyday you would see them.. well.. everyday towing, but they typically are not.
Fuel efficiency that you lose whilst towing you would gain on the other 99% of your kms.
I live in a country where everyone buys used cars from western Europe and it's semi-common knowledge among car people that you should avoid Dutch cars with tow hitches (and the used car yards that bring their cars from Holland tend to have the worst reputation).
That said, if you only tow heavy loads maybe a thousand, tow thousand kilometers a year, it doesn't really matter. It's prolonged heavy towing that kills the small car.
Anyway, my midsize diesel car can tow way more than I personally am legally allowed to and I prefer throwing a tent in the trunk to towing a camper, so my car sees maybe <500 km of light-weight towing a year and under a metric ton you can barely feel the hit to fuel efficiency or performance (because diesel torque is ridiculous)
Really? Home Depot and Sunbelt Tool Rental doesn't deliver around here. You have to pick that shit up yourself, and they will check the gross towing weight before they'll let you hook up. I've towed a wood chipper from Sunbelt with a Civic, and it was pretty much the maximum that the car would tow.
Well, except for the part where then engine skipped timing and died a terrible death few months later. So, I dunno, did it really meet my need? Or was the engine failure purely coincidental? I do know that the mountain roads around here are pretty rough on cars in general; towing at your max capacity while going up a steep grade probably isn't very good for an engine.
Renting a truck would have been far, far cheaper than what I spent replacing the engine.
I don't know your car, it's possible. I'm not here to judge people on their needs analysis, I'm here to judge people for not doing a needs analysis.
The point is people should buy vehicles based on needs not wants. The chance of maybe towing a thing up a hill one time in a 15 year vehicle lifetime is probably not a satiasficing for a vehicle that's primarily used to travel 8.7km each way for a commute and a 1.8km round trip for groceries 5.43 times per month. (Canadian figures).