Weaknesses of Access in no particular order: very poor multi-user/multi-device-access features. No real concept of servers. Buggy, had a nasty habit of corrupting its custom file format causing data loss (Excel never does this). Does expect you to understand SQL, data normalisation, etc. VBA just about serviceable for a spreadsheet but not good enough for a 'real' database-backed app.
Probably someone could try and make a better Access. There are surely lots of startups doing that already, along with hosting. All the "no code" tools that are out there, etc. Access had the advantage of coming with Office so lots of people had it already, whereas today's subscription based services that host your data have incremental cost.