I don't think that phones are secure, but people do use them for things like 2-factor authentication. I suppose that it is the form-factor that is more relevant, since most phones are smaller than a TI-83, so much so that people are willing to carry them around everywhere.

Ultimately, what I envision would be a cross between a Blackberry (size, QWERTY keyboard) and the TI-83 (focus on being a simpler, lower-end computer). Heck, one may as well give it a unix-like OS and leave out wireless communications and sophisticated graphics. I think this is feasible, but the market would be quite small.