I'd switch to square, but since I don't have a debit card I can't use it. I can still use paypal (and annoy my friends in the process.)

EDIT:

To answer your question, paypal still exists for the same reasons banks exist when people hate them, and for similar reasons to why you'd hire a tour company or local guide when visiting a different country. They are embedded -- they offer increased access via established agreements with more financial entities. They have more mastery of the regulatory landscape than their competitors (especially startups).

Finance is in many ways very traditional business, and paypal has invested in traditional parts of business. I'd bet they employ more lawyers than any other payment startup out there, for example.