The carriage question, answered plainly
The stations above serve the Los Angeles market — that is public record. Whether any of them appears in a given lineup is a different question, and not one this site answers, because per-market local carriage is not published here. The 231 US networks enumerated on the channel list are national feeds, and the local broadcast category is counted at zero rather than left to imply something.
Treat that as the standard to hold every provider to rather than as a shortcoming peculiar to this one. Local rights are sold market by market, so a service that claims all US locals everywhere has either bought 210 separate arrangements or is not describing what it actually sells.
Mount Wilson, and why your neighbour's reception is not yours
Nearly every Los Angeles station transmits from Mount Wilson, which makes reception unusually predictable in one sense and unusually local in another. On the flat basin an indoor antenna typically works well. In the canyons, in the valleys behind a ridge, and anywhere with a hill between you and the mountain, it can fail entirely while a house half a mile away has a perfect picture.
Terrain matters far more than mileage here, which is the opposite of the intuition most people bring from flatter markets. Buy something returnable, try it against a window facing the San Gabriels, and find out in an afternoon rather than reasoning about it.
The Dodgers are the cautionary tale this whole page is about
For much of the last decade, a very large share of Los Angeles households could not watch the Dodgers at any price, because the team's games sat on a regional network that most local providers had not agreed to carry. Nothing was technically broken. The games were being produced and transmitted; the carriage deal simply did not exist.
That is the clearest illustration available of what this page is arguing. Whether you can watch a team in your own city is a commercial arrangement between two companies, and no amount of bandwidth, hardware or channel count changes it. It is also why a lineup advertised in the tens of thousands tells you nothing about the one network you actually care about.
What to settle before you subscribe to anything
Decide which of the two problems you actually have. If it is local news and network programming, an antenna solves it for a one-off cost and you do not need a subscription for that part at all. If it is a specific team, identify the network that holds them from the table above and confirm carriage by name.
Doing it in that order saves the common Los Angeles mistake, which is paying monthly for a large lineup to get channels that were free, and still not getting the team that prompted the whole exercise.