Adding a bigger battery to those isn't a whole lot of increased complexity. The only issue is making a PHEV that has the same performance characteristics in both EV and hybrid mode - not that it hasn't been done. Specifically on HSD cars, the two electric motors combined, or even just MG2 (the "motor") have way more power than you'd assume - they actually function as an AC-AC converter, converting a significant portion of the engine's output power from mechanical to electric and back to mechanical again. It's essentially the way the eCVT works. Therefore, with a battery (and buck-boost converter) that can support such a load, they can propel the car alone way more than adequately - with a speed limit to protect the "generator" from too high RPM, due to the way the HSD works.
Anyways, it absolutely can be done and it absolutely can be way simpler. If it's a case of a typical modern ICE with a big battery and a motor thrown in somewhere that makes it "hybrid"-ish - i.e. all the ICE complexity + the EV "complexity" (minus the classic starter/alternator) - yeah, no thanks.
IMO: Good examples - the Chrysler Pacifica PHEV. Bad examples - C63 AMG (the PHEV version).