I don't have much 'vintage' stuff on my bench because it's generally bigger, heavier, less efficient, less featured, etc., but there are good reasons to keep the older stuff, especially as a hobbyist. Part of it is the idea of restoring older equipment - both for the equipment and for the experience of doing it yourself - is an appealing one, and especially with the tendency towards publishing less and less service information, is often easier to actually do with older equipment. Then usually, hobby usage is not pushing the limits of measurement 20-50 years ago, so older gear is up for the task, so if you can get it for a cheaper price than modern stuff, you can either save money or get more equipment (and we all know it's usually the latter). Then for some applications, there are actually fewer dedicated options among new equipment - not because new techniques can't do it, but because it's been rolled in as a software option to something else and the demand for the task has gone down - sometimes having a dedicated meter to tell you the thing you want is easier/simpler/cheaper than finding a modern instrument that happens to have the option you need for that measurement.
Then you get to build quality, and while test gear is generally built to a more lasting standard than consumer gear, getting higher end older gear for a similar price to the lower end new gear often has a better longevity proposition - maybe it needs work now that the new won't, but it's often over-engineered to a degree deemed unnecessary in more modern, mid to low end gear, which pays dividends in long term stability, repairability, durability, or just ease of use (though I am all for manufacturers actually paying attention to UI innovations from others and not just throwing something 'functional' in there). There's also the fact that a lot of hobbyists are people who have gotten to the point in their life where they have more disposable income and time on their hands, and they remember working with (or lusting after) equipment that's dated by today's expectations. If it's something you always wanted or something you're already familiar with using, those are both good reasons to go with the older gear over the new.
Of course, then there's also the value of systems integration and monitoring through more modern interfaces, the ability to find replacement parts, the extra features, and especially, the built in analysis options found on more modern stuff thanks to the ubiquitous nature of memory and processing power now - reasons for me to avoid a lot of stuff pre mid-90s or so for my own use, but there's a reasonable argument to be made for working on and with older equipment.