Striker actually doesn’t come from MMOs - the term there is DPS. Tank does, but 4e used “defender” rather than tank. In fact, none of the combat roles in 4e used the same terms as their typical MMO analogues.
It’s pretty reciprocal. The idea of the party healer absolutely originated with D&D and was adopted by CRPGs and later MMORPGs. And while the terminology of “tank, DPS, and healer” comes from MMOs, fundamentally it’s the same concept as mixed unit tactics, which goes back to war gaming (and, you know, actual war).
4e was the only edition of D&D to really codify these roles, but that’s because it was re-thinking what “class” meant. Instead of character archetypes, 4e classes were a combination of “where your powers come from” and “what your (combat) powers do.” While there’s certainly MMO influence there, it works pretty differently than MMOs typically do. I can see how it would seem limiting in a traditional D&D framework, but you kind of have to treat it as a different game. It does the thing it’s designed to do very well, it just might not have been designed to do what you may expect it to do coming from an old school D&D background.