(1) why are relationships(ie:foreign keys) in RDBMS even useful?
First off, I think you are talking about foreign key CONSTRAINTS. Foreign keys are just a logical design feature that says that this entity matches up with that one.
The reason foreign key constraints are useful are:
They help you adhere to the DRY (Don't repeat yourself) principle. Sure your app validates the relationship, but does it do it in several places? Are there multiple apps that access the same DB? Do you have to repeat the logic in each app? Hey, you could pull that logic out and use a common DLL for access to that data that enforces that logic.Better yet, what if that was built into the RDMBS so I didn't have to write custom code to do something so routine? Bam. Foreign key constraints.
If your app enforces the foreign key validations, how do you force users who are working directly in the DB to honor your rules? I know, I know. You shouldn't let users into the back-end directly, but you just try telling that to the data analysts when they have a project for corporate and you are the bottleneck.
As to the vague error. Wouldn't your argument be better stated as RDBMS X has vague errors when data fails foreign key constraint checks? The way you have generalized it, you could also argue that we should use paper ledgers instead of computers because the constraint had a vague error.
(2) Was there a point in the past where RDBMS were useful for some reason or is there a reason they are useful now that I'm not aware of?
Yeah, that would be now, yesterday and probably long into the future.
I could go on forever about the reasons, but here is the big one...
It provides a common structured file format that is easy to extend, leverage by other applications. You may be too young to remember when every dang system had it's own proprietary structured file format, but it sucked. Plus, it forced you re-invent the wheel constantly in terms of things like indexing, a query language, locking, etc.