In my own heart, I felt it would have been greedy to have insisted on it just because I could. 

The only exceptions are: (1) the parties have a prenuptial or postnuptial written agreement; (2) a free trader agreement; or (3) a court order.How does my seller go about getting a court order?

Then, don't get greedy.

"Be greedy when others are fearful and be fearful when others are greedy."

This will come with all the same costs as when you first bought the house: closing costs, loan origination fees, banks-are-greedy fees and so on.The reason a refinance/second-mortgage can be beneficial is because you have (a) built in equity over time and can access that in the form of liquid cash and/or (b) the house has appreciated over time giving you access to more cash that you didn't invest as equity but earned as "interest" and/or (c) you are able to finance at a cheaper interest rate to save money down the road and have a cheaper monthly payment.

Be fearful when others are greedy.

Follow and learn from Zuber.I also suggest you decide if you want to be a trader or an investor.

Upon their deaths (which happened simultaneously; 'The Notebook' style), their lovely building was worth $10M and you inherited the property and sold for market value (you greedy SOB) with zero capital gains due because your basis in the property was 'stepped up' to $10M (I don't know the specifics of estate taxes but I think they kick in over $11.58M). 

When presented with a good opportunity, they got greedy.

As for evil, greedy LLs, this site goes a long way in perpetuating that stereotype.