Random access to large files is a legitimate use case! LMDB [1] uses a similar technique, and it works well for them. But depending on the specific application, explicitly application-managed caching via O_DIRECT IO with something like threaded pread or AIO might be even better, because with this explicit model, you control the cache sizing and eviction policy, and it's certainly possible with application-level knowledge to do better than the generic kernel-level LRU/active/inactive/kinda-sorta-works-heuristic stuff can do without application-specific knowledge.
Another advantage of using application-managed caching is the ability to take advantage of things like huge pages (which can drastically reduce TLB miss rates), whereas with conventional mmap of conventional files, you're limited to regular 4kB (or whatever) small pages and associated management overhead. (There's no reason in principle filesystems can't use huge pages for page cache, but AFAIK, nobody does it yet.)
OTOH, kernel management of page cache allows for better integration of cache eviction with system memory pressure signals and allows for multiple users of a single file to share the memory mirroring the contents of that file.
> Do you think in this case using mmap could in theory introduce performance gains?
It depends. The right approach depends on a lot of factors, including workload and developer complexity budget. It's funny, really: the more experience you get, the less likely you are to say "$SOLUTION is the bestest evar!" and the more often you say "well, it really depends, so I can't give you an answer".
What really strikes me as needless is someone using mmap to read a 10kB ~/.myapplication.lol.ini file or something.
[1] http://www.lmdb.tech/doc/