The FCC, wanting to be fair to both NBC and CBS, granted commercial licenses to their NYC stations starting the same day, July 1, 1941. Apparently NBC got a leg up on CBS by signing on an hour before normal on that day. So we can say that WNBT was the first commercially licensed TV station in America. And it also broadcast the first TV commercial, a ticking watch with the words "Bulova Watch Time" seen on the screen as we could read the time from the watch.
NBC's NYC station already had a daily schedule in 1939, even as an experimental station, to coincide with the RCA exhibit at the 1939 World's Fair. But CBS had already done some TV shows as early as 1931, featuring Kate Smith and George Gershwin, although that was using an older TV system. And General Electric, on the station that became WRGB Schenectady, is credited with broadcasting the first TV drama, when it televised a community theater play in 1928. That was only a few years after WGY Radio got its commercial license.
So TV really wasn't that far behind radio. But WWII really slowed down the development of television. Lots of people were buying radios in the 1920s but it wasn't till 1950, or at least the late 40s, before some families had a TV in the home. My dad says he and his friends would go to a bar to watch sporting events on TV several years before his family had a TV of their own.