The problem is that a deterministic regex engine (deterministic finite automata or DFA) is strictly less powerful than a non-deterministic one (NFA). DFA's can't backtrack, for example. In addition, DFA's can be quite a bit slower for certain inputs and matches.
"You are technically correct. The best kind of correct."
In theory, your statement is perfectly correct. However, quoting that reference:
"However, if the NFA has n states, the resulting DFA may have up to 2^n states, an exponentially larger number, which sometimes makes the construction impractical for large NFAs."
This means that in practice, DFAs are larger, slower, and sometimes can't be run at all if complex enough.
However, this was my mistake. I remembered (vaguely) the 2^n issue and didn't follow up to make sure I was accurate.
And I completely spaced on the fact that neither NFA's nor DFA's handle backreferences without extension.
I don't know what you mean by "DFA's can't backtrack". Maybe you mean DFAs don't support backreferences, which is true, but NFAs don't support backreferences either.
I believe if r is the size of the regex and d is the size of the data, an NFA is O(r) to compile and O(rd) to execute, while a DFA is O(2^r) to compile and O(d) to execute. So DFAs are slower to compile, but faster to execute.
“regular expression” has different meaning in programming context and formal language context. Regular expressions in regex libraries do more than match regular languages.
PCRE can recognize also all context free languages and some subset of context-sensitive languages. Just having backreferences makes the problem NP-hard.
