I think the length and weight of the trailer will determine if it should be single or tandem axle.
For what it's worth, my parents towed this 18 foot, 1963 Phoenix travel trailer for years and never had a problem. It's a single axle. I never thought about it when I was a kid. It wasn't until I considered purchasing my first TT that the tandem axles became a consideration, and that was actually AFTER we purchased it.
Now, if you look at the set-up my dad had in 1963 (I think the year of this photo is 1965), it was towed with a 1963 Pontiac station wagon. I remember Dad has air bags added to the rear shocks. He always used weight distribution bars, but sway control was unthinkable back then.
We traveled all over the country, from New York, to Florida, to Wisconsin, to South Texas for at least 7 years (from the time I was 8 to 15 years old). I do not remember ever having issues with the camper. He never said a word about sway, concerns about flat tires (although I do remember a flat on the car once ... and a water pump going out in Wisconsin).
I've seen lots of new trailers (although smaller in size than mine) with single axles. I would honestly believe, that with proper hitching, a single axle would do just fine.
