The way I look at it, the tube's job is to contain air and give you a way to add & take out air. It is the tire's job, among other things, to resist punctures. Once a sharp object has gotten past the tire's defences, there's little any tube can do to resist getting punctured. I suppose thickwall tubes are somewhat more resistant to pinch flats, but that risk can be managed with proper inflation & riding caution.
That said, I think the standard thickness is most practical, unless there is a requirement for absolute minimum weight. I think the thinwall tubes are impractical for utilitarian use since they're more easily damaged during installation & removal, & somewhat more prone to getting caught between the bead and the rim.
Since I'm a cheapskate, I'm quite happy to keep patching a tube indefinitely & return it to service after a puncture; so for me, the usual end of life event for a tube is when it develops a leak between the valvestem and the tube proper. I find Presta valve tubes to be noticably more frail than Schraeder tubes in this regard.
BTW, Nashbar & Performance Bike continue to supply their house branded tires in 27x1-1/4, which are about the same actual width as Paselas 27x1-1/8. I don't recall now if they still offer anything smaller, but don't see much need for tires narrower than this (other than for appearance sake, see below) on a vintage bike that will be ridden. If you're serious about racing and want the über narrow tires, get some 700C wheels. I have a few 27x1 tires in my stash, that I will consume on my Motobecane Grand Jubilé, which has the narrow Rigida AL 1320 rims as shown below, but 27" not 700C. I would agree that rims this narrow look a little "funny" combined with a tire wider than 1".