There's no reason to not sanitize data from the client, yet every reason to sanitize it.
Something that's sanitized from an HTML standpoint is not necessarily sanitized for native desktop & mobile applications, client UI frameworks, etc. For example, with Cloudflare's CloudBleed security incident, malformed img tags sent by origin servers (which weren't themselves by themselves unsafe in browsers) caused their edge servers to append garbage (including miscellaneous secure data) from heap memory to some requests that got indexed by search engines.
Sanitization is always the sole responsibility of the consumer of the content to make sure it presents any inbound data safely. Sometimes the "consumer" is colocated on the server (e.g. for server rendered HTML + no native/API users) but many times it's not.
No. I'm making decisions on what is safe for my server. I'm a back end guy, I don't really care about your front end code. I will never deem your front end code's requests as trustworthy. If the front end code cannot properly handle encoding, the back end code will do what it needs to do to not allow stupid string injection attacks. I don't know where your request has been. Just because you think it came from your code in the browser does not mean that was the last place it was altered before hitting the back end.
User-generated content shouldn't be trusted in that way (inbound requests from client, data fields authored by users, etc.)
Unless you're doing something stupid like concatenating strings into SQL queries, there's no need to "sanitize" anything going into a database. SQL injection is a solved problem.
Coming from the database and sending to the client, sure. But unless you're doing something stupid like concatenating strings into SQL statements it hasn't been necessary to "sanitize" data going into a database in ages.
Edit: I didn't realize until I reread this comment that I repeated part of it twice, but I'm keeping it in because it bears repeating.
Other than SQL injection there is command or log injection, file names need to be sanitized or any user uploaded content for XSS and that includes images. Any incoming JSON data should be sanitized, extra fields removed etc.
Log injection is a pretty nasty sort of hack that depending on how the logs are processed can lead to XSS or Command injection