A similar thing happened in some South American countries with a cholera outbreak. Strains that made people more sick forced them to stay inside whereas the more harmless strains allowed people to socialize more and the harmless ones ended up spreading faster
What are the ethics in engineering a new virus and deliberately infecting people? What happens if some of those people die? What happens if your variant that has been engineered to spread extremely effectively mutates into something more lethal? How do you test your engineered virus? Large-scale tests on people? How would that be faster or more effective than producing a new vaccine and testing that instead? What happens if your tests show that the engineered virus is not as benevolent as you hoped, and is actually rather horrific? Can you put the genie back in the bottle?
This alone should make it a non-option, there will be no way to contain it or stop it from mutating, I fail to see how it wouldn't just be a question of time the same way COVID variants are. The consequences could be disastrous and simply worsen the situation.