I believe it's new IRS rules that prompted PP to start asking for a SS# when signing up. I opened my account years ago and didn't have to provide it back then.
Now if you hit 200 payments and $20,000 in sales in one calendar year they have to send a report to the IRS, so I guess they figure it's easiest to have the info on file from the start.
I got close to the 200 payments last year and every time I logged in I got a notification asking for my SS# and saying my account would be limited if I didn't provide it. I was nowhere near the $20,000 though, and I knew the rule was both, not either/or, so I just ignored the notice and after the new year it fell off.
As much as I love the convenience of a PP account I don't know that I'd open one if providing a SS# is a requirement now.