I assume you are thinking about (hyper-)realistic renderings of real life persons, not cartoons ("When the technology became available"). Of course cartoons of real life persons exist.
For realistic renderings the technology is just not there yet at reasonable costs. The development up to the level of realism needed to be convincing is not linear; neither in pure tech nor in perception. The technical aspect is simply the pareto principle, the so called 80:20 rule. You can reach 80 percent of the goal with 20 percent of the effort. But then you need four times the effort already invested for the last fifth of the way. Of course these are not mathematical exact numbers; most of the time the ratio is worse and grows exponentially when getting closer to the goal.
In short: It is easy to do somehow human-looking animated models but is (still) extremely expensive to build real good ones that people will take for humans.
This leads to the famous uncanny valley effect. It basically describes that people will enjoy caricatures or cartoons of real humans; and of course they can be tricked with enough effort. But there is range in between where the animated models don't look like caricatures but like real humans - but not good enough in the details, e.g. the moving of the skin or subtle gestures. And that is something that people can't cope with. It feels uncanny not to know if it is a real person or an animation. So it is not enough to pour more money on the animation department but sometimes you have to hold them back to do something that isn't completely possible yet. Do something right. A good cartoon or a completely convincing rendering of a human. We are not there for the latter (at reasonable costs for normal movies). We will be in a few years and film making will change a lot then. So the premise of your question is not correct: "When the technology became available" It didn't become available yet (at reasonable costs, but tech is not the only limiting factor).
The Polar Express is a prime example for the uncanny valley effect. The movie makers did want to make a realistic model of Tom Hanks but you can feel in every moment that he is not. This makes it a quite scary movie.
Avatar is an example how this effect can be avoided. The humans in the movie are real life actors, the aliens are "realistic" renderings. With aliens that are not supposed to be convincing humans the effect doesn't occur. The aliens have human features so you can relate to their acting (two legs, two arms, head, normal body...) but you don't expect them to be human in every aspect. So you can just increase the quality of animation there without any backfiring effect.
The legal part of your question is hard and highly dependent on the legislation where you produce or distribute the movie. In general you have personality rights even for caricatures or renderings when your person can be clearly recognized or is even called by name. And that is the whole point of using stars in the first place. If it is about an "invented" character (think Borat, Ziggy Stardust or such) the normal copyright and intellectual property rules apply, those are protected.
