It makes sense based on how services work.
Services start by contacting the utility and asking "What sizes of service can you offer me?" The utility looks at engineering data based on the installed plant in your area, and their policies, and says "We can offer you sizes A, B or C".
You choose one that is larger than your house's Load Calculation, e.g. "I'll take B".
And then they say "Alright, here is a list of approved meter pans for B".
The other components are approved by the AHJ, based on NEC rules as locally amended. What does "B" even mean? It defines the main breaker size. If B is "200A" and the PoCo comes out to connect the service drop and finds a 175A breaker in there, fine. If 225A, they won't connect.
Your main breaker is the only overcurrent protection for the service. (kinda makes sense; why have two).
To swap the meter pan, the power company must come and remove their service drop wires. Then, the pan is de-energized and can be exchanged. When the electrician is finished, the power company returns, and re-connects power if the work passes inspection. Notifying the power company and securing permits and inspections is part of electrician's job and it's "tick the boxes" for them, they do it all the time.
What your electrician is saying
First they are saying "I know this power company, and 225A isn't on the menu". He might be wrong, they might be willing to work with you. But most likely he is right; most likely the next size up is "Class 320" 400A service.
The electrician is correct that the normal way to provision "Class 320" 400A service is to have the meter split to two 200A main panels. However, those meter pans accommodate two cables up to 300 kcmil each (to feed two panels NOT for paralleling), and that certainly will accommodate one 250 kcmil cable needed for a 225A service. I can't see a problem with that setup, except that it makes poor use of the service available, so wouldn't normally be done.
Keep in mind right now the electrician business is a seller's market - there's a building and home improvement boom, and electricians get to pick and choose jobs.
While your theory is more fun, facts are different. First, the electrician wants to offer a "soup to nuts" warranty on the work, so that warranty woprk is hassle-free, as you'll demand. Using your own gear breaks their ability to get labor compensation from the supplier. So you must pay it. This gets VERY awkward. Second, 90% of the time the consumer buys equipment, it's the wrong thing. And that must be explained to the suspicious customer. So using customer-supplied gear is the road to perdition for the professional. In this market, walk away from customers like that.
Electricians don't stock parts. That's why electrical supply houses open at 7 am.
