The big one is that running a browser other than Chrome (or Safari) could come to mean endless captchas, degrading the experience. "Chrome doesn't have as many captchas" is a pretty good hook.
I don't know what you mean by "the market".
What I do know is that if I try to go to a site with my favourite browser and a site blocks me because it's so poorly engineered it thinks I am a bot just because I'm not using Chrome, then it's pretty obvious that it's not detecting bots.
Also worth noting: it might surprise you that there browser automation frameworks. Some of them, such as Selenium, support Chrome.
You can add an exception in Firefox's settings to allow third-party cookies for CAPTCHAs. Google's reCAPTCHA cookie is set by "recaptcha.net", and CloudFlare's CAPTCHA has exactly the same problem, whose domain is "challenges.cloudflare.com".
If the cookies aren't set and passed back, then they can't know that you've solved it, so you get another one.
Maybe my experience is atypical but it seems to me this is a reCAPTCHA problem, not a Mozilla one. It’s Google’s problem. I imagine they can solve this but simply don’t want to.
Maybe I’m wrong but again, i encounter more issues with their “anti bot” methods than any other by a massive margin.
It's already a pretty degraded experience.