* The alumni network has gotten steadily more valuable
* The signaling value of being accepted into YC has increased dramatically
* YC's direct influence on investors has increased steadily
* The incentives to apply to YC have increased accordingly, setting up a virtuous cycle (you had to be a bit of an oddball to be in that first class)
* Each batch now funds many more companies than YC did in its entire first year
Meanwhile: it takes lots of years to get to a point where you're ready to file S-1; since the nuclear winter in 2001, you need to be doing a huge amount of revenue with a profitability that can be modeled in simple Excel spreadsheets to do it.
So if you figure YC hit its stride 5 years ago, the year Stripe applied, they're right on schedule.
Consider: Square was founded in 2009, with gold-plated credentials, has done very well, and is only now filing for IPO.