I think this approach makes sense. I do it myself, and I recommend my clients do it.
Most Website companies want you to have your domain name, website hosting, and email with them.
This is a convenient approach, but like most things that are convenient, there are downsides.
Being strategic and intentional about where your domain name is registered, where you host your Website is hosted, and where your email is hosted puts your business in a stronger position and gives you more control.