I wouldn't give one to a first timer because they don't have the skill to control it. They're just starting out, they think they're invincible, and they have a sports car. They're going to barrel into a hairpin at 90MPH thinking "Olol, sports car, zing right around.". And then they're in a tree. The lack of power will have no bearing on this, Miatas can and will go fast enough to exceed the tires' capability to hold the road, and first-time drivers simply do not know how to handle a car when they get near the limit. Just look at how many teens manage to hit a tree in an 89HP CR-X.
A second car? Sure. They're great cars, and someone with enough experience to know when they're approaching the limit will enjoy the hell out of one. I'm buying one myself once I have the steady income necessary to make the payments. But I would never give one to a teen who's license is still warm.
and someone with enough experience to know when they're approaching the limit
That applies to EVERY driver, and EVERY car. You're making a generalization out of something that's already generalized. Whether it be a Miata, an Accord, an Altima, any first time driver in their first car is going to be stupid, is going to take risks, and over assess their ability. My first car was a Miata, and not once did I lose control of it. I drove more aggressively than I should have for my skill level, and took risks that tested the car's limits. I would have done the same in ANY car.