Well, for the owner's it's a sense of pride over all the hard work they've gone through to get to the point of being able to put their business name on the wall. Why do people buy flashy sports cars? To show off success.
I don't think having a name on a building like "SomeGuy's Sawmill" is really an advert, if anything, it's a brand.
Not to mention, say you're trying to find a location like the closest clothing store, or restaurant. How will you locate it (or the right one) if every building is just plain and looks exactly the same?
No-one is saying you can't have a nice sports car, nor that you can't be proud of it - here they're saying that you can't put spotlights on it and erect a hoarding saying "I'm awesome, look this is my car", just park it on the street like everyone else.
How will you locate a building. Numbers, street names - map or GPS : those are the usual way.
That would only work if you knew ahead of time you were specifically looking for that particular location. There's been plenty of times I've driven by some place and decided to go take a peek inside just based on their name alone.
If 'Al' wasn't able to put his business name on the building (or advertise in any form), then he'd probably not make very many sales.
It surprises me where the conversation has gone -- this being HN and all, we're mostly startup/biz/tech people round these parts.
I guess plain signs reading "bakery", "clothes", "cars", "hipster coffee", etc. could be allowed if you try this.