That [currently] is not Zenefits' business model. Their entire premise is that you can practically use any providers you want for your benefits such as various 401K providers, various health care plans, etc., as well as any payroll vendor. Zenefits makes its money as a broker when you choose to go through Zenefits to get things such as payroll or benefits administration services. But the key is that Zenefits itself is not providing the said services. They are paid on commission or rev. share with the providers that ultimately service Zenefits customers.

While they could become a payroll provider themselves, that isn't really their mission. As well, it's not so trivial to write some software "over the weekend" and have a solid payroll system. While payroll companies actually have very little regulation (this is true, and somewhat surprising), it is complex to build a payroll system that can accommodate all the various needs of clients. Just to name a few things to get started: Hourly, salary, pay cycles, 1099, fed/state/local taxes and tax codes and rates, time off tracking, punch in/punch out, check printing and electronic deposit, paper and electronic tax filing, tax payments, garnishments, time off tracking, pre/post-tax deductions, worker's compensation rates, union dues, and the list just goes on from there.

There sure is. I've got a tiny bit of experience with ZenPayroll, and they're separately licensed in the states they're permitted to operate in (and it's a minority of states, IIRC).