Why Google asks for it at all
Verification is Google checking that a real business exists where it says it does. That step needs a real address, and there's no way around it. Working out of your house is fine; plenty of trades do, and Google has a setting for exactly this.
Once you're verified, you tell Google you deliver to your customers rather than serve them at your address, and the address comes off the public listing. Google keeps it on file. Nobody searching sees it.
What people can still see
Your business name, your phone number, your hours, your reviews, your photos and the list of towns you serve. That's everything a customer needs to decide, and none of it points at where you sleep.
What changes is the pin. A hidden address means no exact spot on the map and no directions button, which is right for a business nobody should drive to anyway.
When you should show it
Show it if customers come to you: a showroom, a yard where people pick up material, an office somebody can walk into during your posted hours. In that case the address is a feature, and hiding it costs you walk-ins.
A hybrid works too. If people can come to the shop and you also drive out, you can show the address and set a service area at the same time. What you can't do is post hours for a place nobody is at.
The thing that goes wrong
The common mistake is leaving a home address visible for years without deciding, and then finding it printed on a dozen directory sites that copied the listing. Cleaning that up later is slow and never quite finishes.
The other one is inventing an address to look bigger or to sit in a better town. Google's rules require a real staffed location, and a listing at an address you can't back up gets suspended. Decide once, at setup, and the problem doesn't start.