Under the UCC a check payable to "John Doe Construction" is no different than a check payable to "John Doe.".
Not certain what bearing it would have on this issue, but I would like to see a citation for that.
The account is going to show "John Doe" as the sole owner so how's the teller going to be confused?
I've been a teller. You get confused when you are supposed to make distinctions when there are no apparent differences. Saying we don't split deposits on business accounts is a rule that can be understood and followed. It also pushes the customer toward the mechanism outlined in Accounting 201 for obtaining any cash necessary to operate his business: Write a check.
Or how is the owner going to embezzle from himself?
Generally it is employees who embezzle money. Sole proprietorships may have one owner, but they oftentimes have several employees.
If we have reason to believe he's under reporting his income we can file a SAR.
Banks that file SARs on activity they could easily eliminate are complicit in that activity. Besides, maintaining good practices is easier than filing SARs.