Not necessarily. Neither Houston nor Los Angeles is known for extensive public transportation options,
This goes to show you how misinformed you are: Los Angeles has has has one of the most comprehensive and fastest growing public transit systems in North America. I can't think of a single method of Public Transportation that is not somehow employed somewhere in Los Angeles.
You're also making the wrong comparison by just looking at the city size. You really need to look at the entire Metropolitan Statistical Area to properly determine rail services to implement. Most of the 10 largest MSAs are covered by existing or planned intercity rail options.
1 New York City-Newark-Jersey City, NY-NJ-PA MSA (Served by the NEC)
2 Los Angeles-Long Beach-Anaheim, CA MSA (Planned California High Speed Rail, Existing Amtrak California services)
3 Chicago-Naperville-Elgin, IL-IN-WI MSA (Heart of the LD transportation network)
4 Dallas-Fort Worth-Arlington, TX MSA (Planned Texas High Speed Rail)
5 Houston-The Woodlands-Sugar Land, TX MSA (Planned Texas High Speed Rail)
6 Washington-Arlington-Alexandria, DC-VA-MD-WV (Served by the NEC)
7 Miami-Fort Lauderdale-Pompano Beach, FL MSA (Brightline, Silver Service, Palmetto)
8 Philadelphia-Camden-Wilmington, PA-NJ-DE-MD MSA (Served by the NEC)
It isn't until you get to the 9th and 10th largest MSAs that rail services fall of a cliff in terms of planned and existing services:
9 Atlanta-Sandy Springs-Alpharetta, GA MSA (Palmetto)
10 Phoenix-Mesa-Chandler, AZ MSA (Debatable service)