I don't think the lending guidelines will be all that much more stringent than before the bubble. Certainly won't see the kind of insanity we saw during the bubble with or without these quasi governmental agencies.
I do think 30 year fixed rate mortgages will disappear. They're essentially unheard of in Europe, where there is no equivalent of Fannie & Freddie.
May well be more variation in rates between good and weak borrowers. Look at car financing rates. Anywhere from 5% up to whatever the law allows. Realistically, other factors will dictate par rates, just like they always have.
If rates do end up being higher, overall, we, as taxpayers, should be happy. That indicates the government support was artificially keeping rates low. OTOH, I'm not optimistic this will keep those who want to make bucks at public expense from continuing to feed at the same trough.
Looking at the long term, inflation adjusted Case Shiller data (sorry, kind of an old chart), prices were roughly flat from the start of the recorded data (1890) until World War 1. 100 is the baseline. From the end of WWI until the end of WWII, prices were also roughly flat, and about 70% of the pre WWI baseline. Then, until the recent bubble, they were again roughly flat at about 110%. Fannie Mae was founded in 1938, and there was lots of money available to kick start the economy post WWII. Sound familiar? So, if Fannie (and Freddie) go away, I do think its possible we would settle at a new norm that is lower than 110%. OTOH, the bubble and all the disruption afterward makes it difficult to predict where we might end up. The demise of these agencies is just one factor.