The low hanging fruit of discovering new physics looks like this. Build a bigger machine to collide particles with even more energy. Observe what comes out. It's a clear direction. Just throw money at the problem and get a result.
That said, LHC cost $4.75 billion that's pretty much nothing compared to the amount of money that gets thrown around in the tech world. So might still be worth it just for the fun of it, even if the discoveries don't have any direct application.
That said, of course particle physics results have direct applications. For instance in speculative commercial applications of Nuclear fusion and also Quantum Computing is connected to particle physics. I mean even GPS systems are based on 4D space time. Not entirely sure if any of that can be directly attributed to research happening in colliders but this is just one part of the field, mainly the experimental part - which can verify/falsify theories or result in new ones.
a prolific amount of software, engineering, and material science has come from CERN, as well spinning off numerous high-tech startups.
If we do find new particles we probably can't use them right away, yes, but that doesn't mean we can't later on. A lot of science has been like that.
By confirming a theory you can use the entire framework to come up with useful ideas. This is what happened to General relativity.
If people only asked "ok, that star is a little bit off, but will that lead us to faster horses?" would look funny in hindsight.
The LHC has been in operation for about 12-14 years, and has been a "thing" from planning onwards for almost 40. It's cost $9B, split between a huge list of countries.
Estimates of waste in the US medical system range from around $500B-$2T annualy. The lower end of that scale would support starting a new, fully funded, project of a similar scale for every state in the US every single year.
At a multi-national, multi-decade scale I just don't think it's actually that much money.
> all for the sake of discovering a tiny subatomic particle that we have no way of using
There are few ways I'd look at this.
One is that fundamental science can bleed into regular use over time, look at lasers. IIRC they had no clear use when invented, but are now absolutely key to so much. While the LHC had a headline goal (at least publicly) it's not just discovering one thing, it's a large tool to test fundamental physics.
Another is that this money and work doesn't go nowhere. People are paid to work on big complex problems, building and designing magnets, detectors, computing systems, software for analysis, etc. A lot of that is not going to be entirely custom, and at the very least supports companies & the supply chain for newer advanced technology. NASA I think occasionally puts out some lists of things that derived from their work.
Beyond that, I think there's value in getting a lot of people in a lot of countries to work together on a broadly non-political goal.