Usually not a phone issue. A plan issue.

For example this sort of thing is used to send a lot of texts or a few texts. It's a two item hurdle. The plan, then a phone. One isn't good without the other.

I'm guessing here you are trying to duplicate something. and it's ilk are out there are at the CTIA show ATT would SMS thousands for lunch money. I can't guess what scale you are reaching for, or if you are just looking for the usual M2M idea.