Unfortunately, your time doesn't scale. Selling your own hours whilst also having to build and maintain a product and/or company is not a great idea. Hiring people to answer the questions is expensive as well. Things that get you a good chunk of money are based on being able to scale ridiculously well. Make once, sell many kind of things. People are not a good product to sell.
In addition, big corp knows the cost of an FTE and they will be translating your support offering back to FTE/hours, a unit they can put a price on. In turn, procurement will make your contract negotiation a living hell.
Better build and sell something they know they need but can only translate to how much value it will bring them / how much costs it will save at the bottom. Negotiating percentage(points) of a large sum of money is easier to sell than cash numbers that they translate to a human being being available to them.
Of course, if you really expect zero support is required and you can get many to sign it can still work out. It doesn't sound like a get rich quick scheme though.