Where does RESPA state that a lender may not require a borrower us a specific title company to close? Does this apply only to purchase transactions?

No where!!!
A lender can chose all the service providers, including the title company on both purchases and refis.

"A lender can chose all the service providers, including the title company on both purchases and refis."

The lender can choose all the service providers unless the Bank is the seller, then they could not choose the title company. Also, the bank can choose all the service providers that are providing services to the bank. IMHO - The Bank would have no right to dictate what title company a borrower can purchase their OTI from as it does not involve the bank.

So, other than the required Affiiated Business Arrangement disclosure if applicable, if the bank tells borrowers, on say large Home Improvement loans, which title company they have to close with, the only down side is that we would be limited to the 10% tolerances. But we would no longer have to provide the required list of services providers for title companies?

I caution you to review your state laws. IL indicates it is not in the best interest of the borrower for the lender to choose the title company on a purchase transaction.