It's like asking if Python still doesn't support running without a garbage collector.
It's a serious database for anything that doesn't require concurrent multiuser access.
sqlite.com seems a pretty good cut off traffic volume, I would guess between 95-99% of all web apps are probably consistently getting less traffic than sqlite.com
Though a cache may have been what most of the traffic is hitting.
Most of the dynamic content is generated by the version control system, Fossil (https://fossil-scm.org/). For example: https://sqlite.org/src/timeline or https://sqlite.org/forum/forum
Fossil is hosted on the same machine as SQLite. Fossil is self-hosting and the Fossil website is 100% dynamically generated. Every HTTP request against https://fossil-scm.org/ does about 200 SQLite queries (give or take - depending on the page).
Since only a single process may write to a database, it would be best if that process were local.
NFSv4 has built-in file locking, which is likely the most preferable protocol. SMBv2 is a massive rewrite of that protocol, and I expect any file locking problems would be addressed (especially as Microsoft sponsored SQLite changes specifically for Windows 10).
Remote readers in explicit read-only mode likely won't hurt, but there is a deeper discussion below.