I'll start by answering the OP's question about how often are classic era bike frames out of alignment. As a builder/painter since the mid 70's, I've done hundreds (thousands probably) of alignments. The answer is most frames are somewhat out of alignment and some seriously out. I've visited many framebuilding places (especially in the UK) in the 70's and most were pretty casual about it with rudimentary tools. Furthermore, the $100/150 retail cost of a painted frame in Europe required those builders to make them quickly. The exception I've found were 80's Japanese frames that always seemed to be spot on. American builders raised the price and standard although not everyone does it perfectly. Where I learned to build at Ellis Briggs in Yorkshire, they had a very nice cast iron fixture/alignment table combination. I took back with me from Manchester much of Johnny Berry's Equipment including his 3' X 4' cast iron table. I've gotten others since but that one is still my main table for alignment. I was very fortunate to get it (and the knowledge of how to use it).
The problem with DIY alignment is figuring out what is the problem. I'm not a fan of Sheldon's string method. So you measure the distance of the string to the seat tube on both sids and there is a discrepancy. What's off? One might think that the rear dropouts are left or right of the center of the frame but how do you know? Maybe the down tube is leaning over to one side or maybe it's the seat tube leaning but not the head tube. Or the other way around. Or both. Or the front triangle is really 90 degrees from the threads of the bottom bracket shell and the dropouts are really off center. So the string method is only telling you something isn't right but it can't tell you where to fix what is wrong. There is a way to DIY if one wants to make a straight edge with an adjustable screw but that is beyond the scope of my post.
Just for your amusement, I'll show a couple of pictures of frames and accessories on my Johnny Berry alignment table. The 1st picture shows a carved lug frame I was making for my nephew. The other picture shows 3 kinds of straight edges with adjustable screws.
some of the accessories to check frame alignment on a cast iron table
a gaggle of straight edges that can be used in checking alignment