(I hear similar complaints from friends who are professors. Professors nowadays seem to have become professional fundraisers who do a little research on the side. It may be time to fix that.)
In an ideal world, you could sell the service of helping professors to prepare their research proposals. You could also keep an eye out for grants which the professors might be interested in, and generally handle the money side of things for professors who would rather be worrying about something else.
However, I don't think this would work, because the professors have no way to pay you. As far as I know, no funding agency will fund you for the cost of contracting someone to prepare your grants for you. And they probably won't want to do it out of their own pocket, because; heck, this kind of service will be really expensive (and professors hate funding their research out of their salaries anyway).
But if you've got another business model, I'm all ears.
I know a company (and its founder) who did exactly that, with success. Apparently research institutions have some buffer funds, and if they have a decent chance of getting more funding, will use them to commission such services. What they did was writing the proposal, proofreading and editing input supplied by partners, then taking a share in the project and dealing with management and documentation. Pretty much exactly what you describe here.
Now there's a startup idea!