I work in the banking industry and I don't see any problem with this. Expecting the NYC pay level while not having to deal with the NYC cost of living is ridiculous. When I just looked at a cost of living difference between Cincinnati and Manhatten it shows that the cost of living is 171% higher in Manhatten. That means to enjoy the same life style I have in Cincinnati with ~$100k salary I would need a $271k salary in Manhatten. For me it would be an even more dramatic difference since I live in a very rural area an hour east of Cincinnati with an even lower cost of living.
My company has an office in Manhatten and I often see positions that are virtually identical to my current one and could be easily be done remotely just like I currently do mine. If I tried to apply for one of those jobs and told them I wanted the Manhatten pay bracket and to keep working from home here in Ohio they would just laugh.
In the past the majority of people with the education an skills that Wall St firms were looking for all moved to NYC to work on Wall St. Now that the past year proved beyond a doubt that these types of jobs can be done remotely a lot of companies will likely look to hire people outside of NYC, but they won't be paying NYC wages for the remote position. It will be a great way for the company to save money by paying a lower wage and by not needing to pay for a massive Manhatten office. The prospective employees will still be able to enjoy the same quality of living by living in a cheaper location.
I think in the long run this can have the same type of effect that the highway system did by allowing people to live further away from the currently overcrowded city cores. There will always be some people who enjoy living in the heart of a busy and vibrant city but there are also many that live in an overcrowded city that would prefer to have more personal space by living outside the city but don't move out of the city because they don't want a long commute to work every day.
As to requiring employees to prove they are vaccinated, I don't see any problem with that. A business should be free to require things like vaccinations if they so choose and the employees should be free to find a new company if they don't agree with the company's policy. If a large number of people want to work for a company that doesn't require vaccinations the market will adjust to benefit those companies and if a large number of employees don't want to work in an office with people who may not be vaccinated the market will adjust to benefit companies that do require vaccination. Personally, I don't think most employees care enough about their company's vaccination policy to change jobs over it. There are a small percentage of people that will only want to work in an office that requires everyone to be vaccinated and a small number of people who will refuse to work for a company that requires them to be vaccinated. Probably 80%, including myself, don't care much either way.