Speaking as a technical user, I don't think I'd use your product for recording my voice. I can do that trivially with a voice recorder utility on any computer, or even my smartphone, for absolutely free, and probably with higher quality than a typical phone line can give me.

What I would consider using this is for having a voice contact form. If I deal with users who might be more accustomed to phoning someone instead of filling out web forms, I might tell them "you can call this number and give your suggestions, feeback, etc". Having an option of leaving a greeting message (and to inform them they're being recorded) would be nice.

If you're a developer, these are trivial to do with Twilio directly, but if people don't want to waste time reimplementing stuff they can outsource to you, it could be useful. There probably are other services which do exactly this, although I'm not aware of their names at the moment, as I hadn't had the need to use them yet.