This is kind of the idea behind shared taxis, which are sometimes called colectivos or jitneys or a hundred other names. They have a semi-fixed route and will drop you near where you want to be. They don't leave their stop until they have enough people to fill the taxi. I think they're usually independently operated. They're already quite popular in some countries, South America and Africa mostly. I used them in Chile and it was a really nice system, fitting the niche between taxis and buses quite well. However, you had to know the name of the neighborhood you wanted to go to, and there was no automation.

I honestly think they could be useful in the US for commuting purposes. Everyone going to the same office park from the same neighborhood could charter a shared taxi and relax instead of drive. Cost would have to be low. I'd use it. Hell, I even had idle thoughts about trying to create it. However, I have neither the capital nor the expertise to make this happen.

Edit: also see Demand Responsive Transit (DRT). It's the western name for this, and it's been tried before for various uses. Getting disabled people to the doctor is a common use in the US. Various European cities have tried this for getting people to train stations. In my opinion, it's never been marketed the right way. Also, the big bus/taxi companies that have tried DRT didn't have the vision or will to make it happen. Nor do the municipal governments that have tried.