Some governments already sniff SNI. I believe Russian ISPs do it to comply with regulations put forth by Roskomnadzor, for example. In cases where they are not sniffed or are not even present, encrypted connections may be blocked entirely. Additionally, websites with individual pages that are blocked may be blocked entirely when HTTPS is used. SNI sniffing is only one part of it.
You are right that disabling SNI could be used in some circumstances to bypass censorship. I operate a website which is blocked in Russia, and I've discovered that it is not blocked if the SNI field is removed. However, my website is the only one hosted on its IP address, so SNI is not necessary in the first place. It may be possible to create a browser extension to selectively disable SNI for certain websites to evade censorship, but it would not always be reliable. I do not know if Firefox's new extension API is sufficiently powerful to modify such low-level behavior.
You can modify the browser to not include SNI, but that would prevent you from connecting to an IP with multiple certificates for multiple domains. A server would have no idea what certificate to present to you when you connect to an ambiguous IP address that hosts multiple domains. SNI exists so the server can respond with the correct certificate. Encrypting SNI by doing opportunistic encryption with the server before even sending SNI would be possible and would protect against a passive adversary, but could fundamentally not protect from an active MITM.