We're running an experiment on this with our small company.
Our core web application consists of a Java backend (40k LOC, plus 12K LOC of tests) and a Typescript/React SPA frontend (12k LOC, zero tests). LOC #s are 'real code' via CLOC. Not a simple CRUD app.
It's fine.
I can't say that this would be fine for everyone. We have a very small team (2 fullstack engineers) with good communication; we keep as much logic as possible in the backend; we have a robust test harness for the backend. Still, it works very well for us. Even without testing the frontend, it is very rare for bugs to hit users.
Our reasoning for skipping frontend tests: Most of the frontend code is visual. Tests can't tell you if the result is aesthetically satisfying, so you have to look at it no matter what. Since the backend diligently enforces data sanity, the frontend can't really get into too much trouble, and a page reload fixes almost anything. Frontend testing seems to be high-effort low-reward.
I don't think this would be possible without Typescript. TSX helps too since the compiler (really the IDE) catches what would otherwise be template errors. Large refactorings are pretty painless.
I would do this again.
I have also reverse engineered about a dozen other company's web applications recently (to automate them), and noticed that there are other app design philosophies that would make this approach difficult. Some teams go with a "smart frontend dumb backend" approach that can produce all sorts of nasty data corruption issues if the frontend screws up. I'm not a fan of this approach but if you take it, I don't think Typescript alone will save you.
This is an example front-end react component project that I wrote that benefits heavily from tests: https://github.com/lookfirst/mui-rff
Why? Because it is a wrapper around two other frameworks (React Final Form and Material-UI). Any time those two frameworks change something in a way that I didn't expect, I want test failures.