In the case of an incredibly rapidly mutating virus like COVID-19 it's just not worth it to go through that whole process every time it goes from hands to claws to hooves.
It's not that it's not worth it, it's that this approach doesn't work. Evolution is a remarkable force, and unless there's a good reason for the part of the virus/bacteria/amoeba you're targeting to stay that way, it will change to escape the selective pressure against it. We're more-or-less seeing this with SARS-CoV2, even though the virus is a relative amateur at genetic drift.
OK, you may say "let's target the vaccine against a part that doesn't change"...that's great, except that those parts tend to be so common -- so "evolutionarily conserved" -- that you see them all over the place, including, often enough...your own body. Train your immune system to (over)react against common antigens, and you're going to cause problems.
The primary reason that vaccine development is difficult is because you have an extremely high bar for effectiveness, coupled with an extremely low bar for side-effects. And even if you find such a unicorn target, you have to make sure it stays magical over time. The mRNA technologies are great and do accelerate things, but ultimately, the speed of the Covid vaccine development process was more about our willingness to throw huge money at the problem and eliminate all development and liability risk, than it was about any particular technology platform.
Nope, the Moderna vaccine was designed in 2 days after getting a full DNA sequencing of the virus. Very rapid design is a particular feature of mRNA vaccines (with the caveat that sequencing to find the right proteins is required).
Said differently: the slow part of creating a vaccine is doing the trials to make sure you have safe and effective target.