We can. The problem:
It can and most likely will eventually mutate to have harmful effects/become dangerous. Then guess what? You, the government, officially released a virus which kills people. And you can stop it about as well as you can stop Covid right now, only you made the disease.
I imagine that won't go over well.
Besides that- It's the ability to replicate that makes covid both dangerous and gives it the ability to spread. Remove the ability to make you sick will also impair it's ability to spread, so it might just putter out and never spread. Trying to genetically create a disease that spreads among humans and doesn't make you sick would require human trials, and that is NOT going to happen in a short period of time, as these aren't easy, well-known vaccine technologies we are talking about (don't even start with "but mRNAs are neeeeewwwww")