Can someone meet me inside the terminal at TPA?

Yes. Ask for a meet and greet and the chauffeur is inside Tampa International Airport at arrivals with your name, rather than circling outside while you look for a plate number.

It is worth it on three occasions in particular: a long international arrival where you would rather not think, anyone travelling alone who would like to be met, and a first visit to a terminal you do not know. It is not worth paying for on a short domestic hop where you know exactly which door you are walking out of.

Either way the car is at the kerb when you reach it. The difference is only whether someone walks you there.