Suppose you manage a thrift shop. You buy used, old stuff from people who empty their garages or their lodges and you usually do so for free: people call you, you pop up at their place with your empty van and leave after a long day of moving boxes around with a full van.
Will you profit from this? Almost certainly yes. You get a lot of free stuff and the probability something valuable is in there is quite high. Moreover, since you get it for free, it doesn't have to be that valuable (we are not talking about gold nuggets), so a good chunk of it will turn into a profit, if small.
Can you improve your profits? Well, you could if you left out the crap and just cherry-picked the nice, valuable stuff. But what if everything is in dusty, closed boxes and you don't have time to open them all and look inside? Nobody is going to call you if it takes you weeks to go through their stuff.
Also, you don't know what the valuable stuff actually is: a man's junk is another man's treasure! So you resort to just have a lot of stuff in your shop, and hope that someone someday might find value in what others discarded.
This is a metaphor for mathematics. A lot of it looks like 'useless crap', and will probably stay that way for a long time, maybe forever. Some of it is clearly useful, though it's often hard to know it in advance since it's usually boxed together with a lot of unassuming, abstract foolishness. Some things are hidden gems: they lurked in the dark corners of mathematics until someone realized they can actually do amazing things. Other things seemed useful for a reason, and then turn out to be useful also in another, completely different context. The problem is, nobody knows which is which.
In short: you never know when your grandma's cohomology theory will be fashionable again.