Given we're talking about APIs, we avoid many of the UX problems, but it feels like taking on a different set of problems than just using a bearer token. It does provide baked in solutions for things like revocation and expiry though.
Web developers in general are more familiar with other forms of authentication so unless you have a strong reason for picking TLS client certificates I would suggest picking something else.
In other words: I would be more likely to try out an API if it was based on Basic Authentication. ;-)
On the other hand some companies use them even for browser clients for passwordless authentication.
TLS client certs are nice if everyone knows what they're doing, but in a lot of orgs that just isn't the case.