I haven't read Greenspan's book, but the subprime mortgage collapse would not have been avoided by more money for regulation, but it needed a different kind of regulation that looked at the big picture rather than focusing on a particular segment of the financial and real estate industries. Fannie and Freddie, for instance, are pretty heavily regulated, but by the time they figured out what was going to happen it was too late.
Regulation would've stopped the banks putting lipstick on the pig, slicing it into fractions and selling it to everyone as AAA securities. Regulation would've stopped banks giving mortgages to people who couldn't afford them (NINJA loans...wtf?). Regulation would've stopped banks writing mortgages and then dumping them - often before the deal had closed - into the aforementioned beautification system, so that they earned originator commission for zero risk.
Separately, Greenspan drove the common wisdom that everyone should own a home (it's the American dream, but not everyone can afford one), which is predicated on the flawed premise that house prices will
always rise. To this end, he had the Federal Reserve lend
our money to banks an zero or near-zero interest rates. He was schilling for home ownership as late as 2008, when the house of cards was already hitting the floor.
So, with all this free money available to the banks, no downside for writing a mortgage to anyone and everyone - regardless of financial standing -inflated profits to be had by writing "sub-prime" mortgages and no one minding the store, it's no wonder the whole thing collapsed.