As a cache, it is. All you need for a cache (if you're using it correctly, as a cache) is for the replica to be up, which it can be. Azure even gives you out-of-the-box multi-AZ replicated Redis with 99.99% promised uptime (and based on previous experience, I'd say they deliver on this promise).

> Adding an extra moving part

I specifically mentioned I considered those as good solutions for the problem at hand only if you already have them/ don't need to add them, that's their strength (lots of systems already use Redis or a SQL database, e.g. Postgres - but anything really would work just fine for the task at hand).