Several large lenders, including JPMorgan Chase, have ceased using MERS for new loans.
If you waited until the eve of closing to inquire as to whether MERS was to me involved in your mortgage security instrument, then you probably already have a serious problem, unless you are merely re-financing. Most real estate purchase and sale agreements contain a financing contingency and well as a contemplated closing date.
The wording of the financing contingency often requires the borrower to apply for financing and to notify the seller by some date certain if acceptable financing cannot be found. When this date passes, usually the buyer/borrower is fully liable and can lose the earnest money deposit if the buyer fails to go forward with the purchase on the contemplated closing date shown in the purchase agreement.
Leaving aside whether an MERS mortgage poses any special perils to you, even supposing that it did, if you have passed the date specified in the financing contingency and the closing date is already approaching, then you are already over a barrel.
You are unlikely to be able to arrange alternative financing in time and refusing to go forward with the transaction is very likely to result in the loss of the earnest money deposit. The lender is very unlikely to deviate from its business practice of closing with an MERS instrument if that is what it is doing. Even if they did refrain from using a MOM instrument, they could always still assign the loan to MERS after the closing so only getting them to agree to write in a non-assignability clause, which they will NEVER DO, would preclude a later assignment.
If the financing contingency has not passed, the surest way to avoid MERS is to use a lender that doesn't involve MERS in the transaction. This will cost you a new application fee, renewed effort preparing the application, etc. It is certainly true that if enough borrower refused to do business with MERS lenders, then these lenders would abandon MERS.
IF it was important to you for your mortgage NOT to be assigned to MERS, then you probably needed to obtain written representations from the lender at application that the loan would NOT be subject to assignment to MERS or at least to use a lender KNOWN not to use MERS.