One more thing...
I think if you really want transit that benefits someone, usually you don't just want them to live near one good route, whether that's heavy rail or just frequent bus. One line will only take you to the places along that line. Most people will have to go to places beyond what one would find along just one line. If they need a car to get to those places, they'll buy a car, and once they have a car already paid for, the likelihood of them benefiting from transit is low. Basically, you need either really bad congestion, really high parking costs at their destination, or really really fast transit.
That's why it's important to not just have one good routes nearby, but a whole network of good routes nearby. If you can't have a good network, probably your best bet is just a BRT to downtown with some park and rides, and maybe dial-a-ride service (some municipalities have found free taxis is cheaper to provide than dial-a-ride). Maybe some very basic bus service for people who really have no choice.
And the high quality frequent network doesn't have to cover the whole city. I'm a half broke car-less student, so I don't do much shopping and my university ("work place") is close by, so I'm not the best example... But my parents who live in a suburb of Toronto and each have a car still do most of their shopping relatively close by. Even though Toronto's sprawl continues for 50-60 miles from where they live, I'd say for 95% of shopping trips, doctor's appointments, etc, they stick to places 5-6 miles away or less. Maybe once a month they'll venture to the big regional mall, or the outlet mall, each about 15 miles away. A couple times a year they might visit a friend in another corner of the city, or go downtown to see a show or museum, but 99% of the time they stick to areas about 15 miles away or less.
Even for commuting, one parent works downtown Toronto and the other in the same suburb they live in. That's pretty typical. It's rare for Torontonians to commute across the metro area. From the outer suburbs to downtown, that happens in moderate numbers. But from the Western suburbs to the Eastern suburbs, or vice versa is very rare. If commuting time wasn't an issue, you might expect 50% of people to work in their half of the metro, and 50% to work in the opposite half. But in Toronto, it's really more like 95%/5%. If you live in the far outer suburbs, it's even less likely you'll commute to the opposite side, it might literally be something like 98%/2%.
I'd imagine Houston is similar. Lower income people might decide it's not worth having a car just to take 1-2 trips a year to the other side of Houston (or to other parts of Texas and the country). Either rent a car, use a friend's/family's, or just forget it and not go there. Middle income might go down to one car. One person might still use it to get to work, but the other might use transit. And if there's teenagers or grandparents living with them, they'd use transit too whereas otherwise they might have their own car, or borrow the parents'.