I didn’t go to university, because I wanted to learn useful stuff, but because I’m curiousity driven. There is so much cool stuff and it’s very cool to learn it. That’s the point of university that it prepares you for a scientific career where the ultimate goal is knowledge not profit maximisation (super idealistically).
Talking about Turing Machines it’s such a fun concept. People use this to build computers out of everything - like really - it became a Sport by this point. When the last Zelda was Released the first question for many was, if they can build a computer inside it.
Does it serve a practical purpose? At the end of the day 99% of the time the answer will be no, we have computing machines built from transistors that are the fastest we know of, lets just use these.
But 1% of the time people recognize something useful… hey we now found out in principle one can build computers from quantum particles… we found an algorithm that could beat classical computers in a certain task… we found a way to actually do this in reality, but it’s more proof of concept (15 = 5×3)… and so on
Maybe OP could also try if he could contribute to existing projects.