What would be a persuasive statement either supporting or opposing a bank's right to assign a mortgage to a third party (for example, a third-party financial institution)?

If you're looking at the bank's actions from the buyer's standpoint, you may argue against the bank's right to assign a mortgage to a third-party lender. However, if you're looking at the bank's actions from the bank's viewpoint, you may support the bank's right to assign a mortgage to a third-party lender of its choice. 
Let's say you're looking at the problem from the buyer's viewpoint. In this case, a persuasive statement opposing a bank's right to sell the mortgage may look something like this:
A bank's unilateral right to sell its mortgages deprives buyers of the right to informed consent.
Ok, let's take a look at the statement. First, buyers who wish to purchase homes can borrow from two types of institutions: mortgage banks and depository institutions (such as commercial banks, credit unions, etc). Mortgage banks and even depository institutions often sell their mortgages on the secondary market, either because they do not have the capital to finance large-scale borrowing or to sustain long-term funding of mortgages.
Banks that sell mortgages to third-party lenders often reap substantial profits from the sale of those mortgages. Although banks must disclose to potential buyers their ability to permanently hold mortgages (in the sales contract), they do not have to involve buyers in the process of choosing third-party lenders. This means that a bank can sell its mortgages to any third-party lender of its choice. Buyers have no say in this matter; the bank may even sell its mortgages to out-of-state third-party lenders without the consent of buyers.
The only thing the bank must do is to ensure that the terms of the loan do not change. Banks actually have a legal obligation to make sure that interest rates and loan terms do not change in the transfer process. Banks can sell its loans in two ways: either the bank will sell servicing rights to its mortgages or the bank can sell both the loan and the servicing rights to its mortgages.
Banks that sell just the servicing rights will continue to make money from the interest paid by buyers. However, buyers will have to rely on third-party lenders for their customer service needs, whether it involves escrow disbursement or loan modifications. Many buyers feel vulnerable because they have been deprived of informed consent. Also, buyers must create new online loan accounts, update bill pay services, complete new paperwork, and inform their towns of a change in lenders each time a loan is sold. It is a process fraught with the potential for human error. In short, the process inconveniences buyers on more than a surface level.
On the other hand, a persuasive statement that supports the right of banks to assign a mortgage to a third-party lender may look something like this:
Banks that sell their mortgages on the secondary market are better able to navigate interest rate fluctuations than banks that don't. 
To back up this statement, please refer to the links below for some ideas.
https://www.investopedia.com/articles/pf/07/secondary_mortgage.asp

https://www.mtgprofessor.com/A%20-%20Type%20of%20Loan%20Provider/why_do_most_lenders_sell_their_mortgages.htm