To use OP as an example, in a lot of places, you'll find an ancient milling machine or a lathe that's dedicated to running a single job a few times a year. The machine was depreciated decades ago, but it can still do that job and there's no reason to get rid of it.
What modern tools give you is speed and flexibility. Many shops need neither.
Seriously though, of course you can make a living with old tools - however, even the village metal workshop around here has at least one big-ass laser cutter and a CNC mill next to all their old(er) lathes, mills, brakes, presses and other toys. Many oldschool fabricators I spoke to over the last few years are quite interested in what laser welding brings/will bring to the table. Basically all smaller fabrication companies I've seen (the long tail of the car industry and other bigger industries, mostly) are continually upgrading their infrastructure with all sorts of robots and other automation widgets. And so on.
It's work that you don't need to do and that you won't get paid for. If the old machine breaks, then maybe it would make sense to move the job to something newer.
I used to work with someone whose entire business was retrofitting old machine tools with modern controllers when the decades-old electronics failed. You'd be amazed how much of this stuff is still out there.
btw: I think I have a reasonably solid idea of a range of fabrication environments, the oldest piece of machinery I'm responsible for in my professional life is about 70 years old (its basic design is decades older) and some of my personal stuff (sewing machines, mostly) is more than 100 years old. I'm really not against using what works at all.
Many of the modern tools can also be grafted onto the old tools. Not just CNC conversions but the biggest productivity boost when I worked in a shop was converting everything to a zero point clamping system.