I think it is a bit of an oversimplification of the assignment of blame. Obviously every case is different and while most would assume a delinquent homeowner stops paying both lenders at the same time, it is not a given.
I think what is missed in your analysis bearish is the importance of what has or has not already been written off. That is, if the second already has written the loan off then what do they care if the home forecloses or not. Lets say there are 20 portfolios written off. In my opinion this has much more bearing on the attitude of the second. Furthermore what you did not mention was the payoff from the first. Take a 400k payoff. Say the first was a 550k loan and the second was 90k. Now the home sells for 430k and after closing there is 400k left. So the first offers 3k to the second and keeps the 397k. So why wouldn’t the second try to get more? Now if they use this strategy on 20 portfolios will they get more by playing hardball rather then rolling over for 3k on each one? Obviously there stats show that the answer is yes.
Anyways yes the total blame does fall on the first but it doesn’t matter if the first forecloses quick or not, the second still needs to release the lien. Perhaps if banks were not all bloated with bailout money seconds would not be playing so much hardball eh?
There is plenty of blame to go around for all parties. I had a short sale once upon a time and the first was Wells Fargo Bank and the second was Wells Home Equity and the whole thing almost crashed and burned because Wells Bank would not give Wells Home Equity more then 3k. It is a joke but a very sad joke.