Cutting out a piece of a slab and sending it to a lab is for post-pour validation in serious construction. There are pre-pour tests that are much simpler depending on the seriousness of what you’re building.
The slump test is rather simple, for example: https://en.wikipedia.org/wiki/Concrete_slump_test
It’s basically a cone with handles and a procedure that’s easy to learn.
This issue here is mainly that it's very expensive to ship all the components of a Concrete in the volume necessary in an economical manner. Some areas of the world just lost the lottery when it comes to having resilient building materials.
Corruption absolutely is an issue as well - I don't mean to downplay it - but even if we remove it as a factor there are just a lot of variables involved in making a reliable Concrete... finding a good mix is an artform and if, for instance, your limestone quary suddenly hits a more clay-laden amalgamation then your Concrete that was reliably lasting for three decades under certain conditions might suddenly lose a decade off the expected lifetime. That change in material quality can also be difficult to detect so there are real quality assurance issues in Concrete mixtures outside of just corruption and cutting corners.
But yeah, there are concrete plants that cut corners and try to save on cement (the most expensive part of the mix), which depending on the project may bite them in the ass when they have to pay to fixing it.