Sinking isn't always a problem - look at Venice! I studied Civ Eng at Plymouth Poly (now a university, Devon not MA) back in 1989ish. Back then concrete cancer was all the rage ... and gabions (but I digress.)
The failure of the building in Miami was catastrophic and not gradual. I don't think that monitoring would have worked but it is possible that stresses/strains built up over time - we'll have to wait and see. If it was gradual then there is a good argument in favour of fitting buildings like that with strain gauges as many bridges are. I do a lot of IoT stuff and I estimate that something like £20,000 would get you strain gauges and a monitoring system for a structure like that. It might be £10,000 or £100,000 but a building that size in Miami is worth quite a lot. I'll bet rent on a flat was something like $2,000pm or more.
Inspection of foundations is a tricky one. I am not a Civil Engineer but I trained for it but I don't have X ray eyes and nor do Miami's engineers. That's absolutely the wrong way to go about this sort of thing. I'm not even sure what an "inspection" even means.
There was a fundamental error made at the initial design stage in my opinion. I don't know what but probably relating to the parameters of the ground that was built on. By that I mean that the architects/struct engrs. were promised certain properties of the geotechnics/geophysics - that basically means they were told how the ground would work in holding their structure up.
When you design a structure, it needs to support itself and crucially, the thing it sits on needs to be able to support that structure. You also have to work to a timespan, so you use standard tables for wind strength, earthquake etc. You work to a 1 in n years events.
This building collapsed catastrophically in seconds without warning. I think this will become a real lesson for Civ Eng and not a simple "I told you so" thing and certainly not "shit concrete".