There's a healthy way to raise the bar and there's lots of unhealthy ones.
A healthy way would be bringing your current talent pool up to a higher level through training, even if that's maths (if that's what your current problem is).
An unhealthy way is introducing a bunch of new talent that is tested on one niche domain of software engineering and pretending everyone needs to do that while also trying to improve fundamental skills that help them with their day to day job.
- you've got people working crazy hours and learned on the job. Are they supposed to spend extra time on this stuff when they're barely keeping up?
- the existing people have developed all sorts of niche skills of their own. I'm not trying the new folks on that stuff because... we don't need more of it right now.
The point is that most of the time you're not actually hiring for specific niche skills that the rest of the team don't have. You just need more capacity to do what the team is already doing. In those cases if your tech test is some Leetcode algorithms question that the team can't pass themselves then asking that of a new hire is silly. You'll be ruling out candidates who could do the job well, just because they can't pass a test you don't need them to pass.
All I suggested is using the team's existing skillset as the measure to hire new people for the team, rather than some sort of arbitrary test that doesn't reflect the work they do.
“we need someone who can help us write our yet another SaaS CRUD app using an MVC framework. But to get the job you have to reverse a binary tree while riding a unicycle on a tightrope juggling bowling balls. We also offer below average pay and make up the difference in statistically worthless ‘equity’ and only want 10x developers who are willing to work for 60 hours a week”
Using a test that you don't have the knowledge to assess is unlikely to raise the bar. It's much more likely to just mean you hire the wrong person.
If you really need to hire someone you can't assess internally then you should seek help with hiring them. This is one reason why networking and mentors are so helpful. Other people can help with this sort of problem.
A healthy way would be bringing your current talent pool up to a higher level through training, even if that's maths (if that's what your current problem is).
An unhealthy way is introducing a bunch of new talent that is tested on one niche domain of software engineering and pretending everyone needs to do that while also trying to improve fundamental skills that help them with their day to day job.