You can and I regularly close tickets for not following the template that says at the very top "tickets not following this template will be closed with no reply".
It's even better if you can get a bot to automatically reply and close it.
I was thinking about how one could automate this when reading.
Not a foolproof way, but add a string in your Issue Templates that is required to be there, e.g. <!-- AUTOMATIC-CHECK -->.
If this is not present in the issue, the GitHub action just closes the issue with a message to please fill in the template if they wish to create an issue.
Doesn't catch nearly everything, but should get some and it's easy to set up. Could be interesting to go further with the idea and maybe check if each section contains text or something like this, hmm...
Another, somewhat more underhanded trick: add a string that is required to not be there, e.g. "Please remove this line entirely.", halfway through the template, and mention it nowhere else.
I've seen this in repos, I'm pretty sure there are bots who implement it. I'd guess it catches more than 90% of cases, especially if you put the string at the bottom of the template.
It's even better if you can get a bot to automatically reply and close it.