Yes, I have been in taxis in Mexico City at night. Many times in many different parts of the city I have procured the services of taxis of all kinds for decades. All of my experiences have been fine and I've never been terrified, scared, concerned, attacked, robbed, worried, or kidnapped in any way.
I have been overcharged, though. It happens less now that I speak the language fluently but I can't change the fact that I'm an obvious foreigner. The city does not regulate nighttime fares.
If you are concerned, get a "sitio" taxi from one of the thousands of convenient taxi stands that check on and track their drivers and cars. It costs a little more but provides rock solid security.
You should never have any trouble with Mexico City transit of any kind except personal cars; driving yourself is insane in a city of 24 million. The transit system, from taxis to subways, is clean, cheap, innovative, reliable, and efficient with an excellent worldwide reputation.
That is accomplished with a network of private regulations (taxi sitios), fully public systems (subway, bus rapid transit), minimal public regulation (taxi licensing), cooperatives of private contractors (minibuses), privatized toll roads, and public streets. As an operators, you can choose the level of regulation you want to operate under and then operate the corresponding kind of transit you want your business or career to involve. Diversity works much better than monopoly of the type being mandated in Vancouver or NYC.