You can indeed have that and many people do, but the problem with going that route is you can only use the lowest common denominator of features of any of the t

You can indeed have that and many people do, but the problem with going that route is you can only use the lowest common denominator of features of any of the target databases, which wipes out a lot of the performance or convenience features you'd get from either. (arguably SQL itself is/was supposed to be that common layer in the first place, but db vendors always want to be able to present users with new features that are not yet standardized)