The catch-phrase of old was legal to start, legal to finish, but that was not the official language in any regulation that I know of. For this example, if push back time plus scheduled time was good, you could continue forever. FAR Part 117 went into effect in about 2014. 117.11(b) says: If unforeseen operational circumstances arise after takeoff that are beyond the certificate holder's control, a flightcrew member may exceed the maximum flight time specified in paragraph (a) of this section and the cumulative flight time limits in 117.23(b) to the extent necessary to safely land the aircraft at the next destination airport or alternate, as appropriate. "Flight time" here includes time spent taxiing.
Note the "after takeoff". There's no longer a free pass on taxi out delays. If you don't get off the ground by an appropriate time to get to your destination, you can't takeoff. 117.19 has another set of rules for duty time, which starts when you get to an airport for your work day, and ends when you leave an airport at the end. That paragraph uses "prior to takeoff", not "prior to taxi", so a similar idea.
Bob