Another argument in favor: don't stick unnecessary levels of separation between you and the company that controls your domain. Only the very largest web hosts are also domain registrars, the rest are simply reselling another company's services. If there are problems, you're stuck dealing with them through a middle-man.

The only advantage to buying both hosting and domain registration from the same company is billing convenience, while there are numerous advantages to not doing so. Just choose an accredited registrar.