Different deal, I think. Tax exempt number lets you buy stuff for your farm without paying sales tax on it. There is no paperwork involved except the store takes your information and keeps it on file. You are thinking of a sales tax permit where you sell stuff and charge sales tax on it. Most folks don't do that for personal sales.
However, those of us who sell at markets and are running a business have to. We have to have a sales tax permit, an egg handlers license, and we have to use new cartons to sell our eggs in, not used. That is the law. And that is why we have to charge more for our eggs to break even.
Although truth be told, everyone who sells eggs is supposed to do that, whether you sell them out your back door or what. But lots of people don't.