As of this year, and limited to three models exclusive to Japan: yes this happens. The new 2023 model year Serena from Nissan uses a generator optimized engine

As of this year, and limited to three models exclusive to Japan: yes this happens. The new 2023 model year Serena from Nissan uses a generator optimized engine in a series hybrid setup. The engine runs at a fixed rpm (except in extreme situations like accelerating a bunch on the highway going from 110 to 140) then it switches to a second higher rpm mode. I bought one, it's a lot of fun to manage the engines heat and battery room. My record is 38km per liter using local driving up and down our hilly community. Pretty incredible when you consider hills are the natural enemy to none hybrid millage. The car accelerates like an EV. And with Japan's expensive electricity I'm paying only about double the millage cost of an EV. Despite the full size minivan costing us about 20k USD new. Most hybrids, and all Toyota ones, are not using a special fixed rpm engines. They use a regular motor with different timings. The Nissan fixed rpm engine is actually less powerful than the electric motor powering the wheels. Thus at max acceleration you can deplete the battery faster than it is charged.