.... and you've just embraced (in a limited inconsistent way). using "ORDER" is outside of the relational model, where order plays no part.
ORDER was there from the beginning, but CTEs, nested columns, window functions, connect-by recursive selects and similar stuff is being added because SQL and the relational model are actually quite limited when it comes to real world problems.
Of course, SQL will keep getting extended to solve real world problems; however, that does not mean SQL is "the best solution out there" (or "the worst solution except all others that were tried").
Regarding ordering. Relations are defined to not be in a meaningful order. This doesn't mean you couldn't define some derivative that is ordered or that the relations might not be ordered in some way that is ignored by the relational math.
Suppose we have a relation R. We may order this relation physically in order to help the computer retrieve data faster, clustering on an index for example. However, clustering on an index does not mean that we are guaranteed to get the same order back when we do a select * from.... (we probably will but we aren't guaranteed to). And if we add a join or other relational transformation, the order will probably not be the same. In other words, ordering is outside the scope of relational math per se.
However that doesn't mean you can't have pre-ordered relations. It just means the ordering is meaningless as far as the math goes. The ordering may however be of great practical importance as the computer goes about grabbing the relevant tuples from the relation.
Similarly I don't see a reason why ordering can't happen after the relational math is done either, in this case for humans.
What this tells me is that the relational model is not entirely complete in itself in that ordering is an orthogonal consideration largely ignored which means there are certain questions you cannot answer directly with relational math (such select from R a relation L such that it includes the tuples with the five highest values of R(2) lower than 25. I think that's mostly what you are getting at. But that's a matter of relational math being incomplete for real-world scenarios, not SQL (since SQL implementations do provide for ordering).
There are certain things I really like about SQL at least compared to other programming languages. I am not sure it is the best possible db query language. Personally I have always thought Quel was elegant. However compared to app languages, I would far rather spend my time debugging 200-1000 line SQL statements than 200-1000 line subroutines in Perl, Ruby, or C++.....
ORDER was there from the beginning, but CTEs, nested columns, window functions, connect-by recursive selects and similar stuff is being added because SQL and the relational model are actually quite limited when it comes to real world problems.
Of course, SQL will keep getting extended to solve real world problems; however, that does not mean SQL is "the best solution out there" (or "the worst solution except all others that were tried").