I don't have my live local CW on AT&T TV either, though YouTube TV carries it. In San Diego, CW is a substation of the CBS affiliate, which recently bought it. I'm not sure DirecTV carries it (I assume they do), though I know for a time Dish Network couldn't be bothered with including it after the station ownership changed a few years ago.
It makes me think that with AT&T TV, it's a matter of tasking people to do the legwork to sign up these less in-demand local stations (outside the big 4 networks that carry major sports). And if there isn't a huge demand from customers, why bother? Not to mention, you can get almost everything for free anyway (on demand on a limited time basis) from PBS and CW via their respective apps. (When I sign in with a free account, I can get local PBS content as well.)
Fortunately, my CBS affiliate (the local news I mostly watch) recently launched a news app for Roku, which includes its live news broadcasts that air on CW (same news team/anchors at different times). I actually can't get CBS/CW via an indoor antenna, though I live in the middle of the city less than 10 miles from the tower and can pick up the ABC affiliate from that same tower. *sigh*
Hmm. I thought the only major local station owner with whom AT&T TV lacked a carriage agreement for their CW and MyNetwork TV affiliates was Nexstar. That accounts for most of those two networks' missing locals in major markets like NYC, LA, Philly, Dallas, Houston, Washington, etc.
In San Diego, KFMB is the local affiliate for CBS, The CW, and MyNetwork TV. They're owned by Tegna. Looks like none of Tegna's local CW or MyNetwork TV stations are carried on AT&T TV, even though their big 4 affiliates are. So that puts them in the same boat as Nexstar. It's just that Nexstar has *way* more CW and MyNetwork TV affiliates than does Tegna, especially in big markets. So I guess there are at least two carriage contracts that DirecTV Stream needs to ink to fill in all their holes in terms of missing CW and MyNetwork TV locals. (Here in Nashville, our local CW and MyNetwork stations, as well as our local Fox, are owned by Sinclair. All of them are on AT&T TV.)
As for picking up KFMB via OTA antenna, well, my first thought was that it's on VHF while the ABC station on the same tower is on UHF. But actually, they're both on VHF; KFMB is on 8 and KFTV is on 10 (although it's also simulcast on UHF 20 -- is that what you're actually getting?). And both 8 and 10 broadcast with similar power. It would be pretty odd if a given antenna could get VHF 10 but not VHF 8. But it might require moving it around the room some (unless it's a bigger antenna).
At any rate, if DirecTV Stream is going to price itself a bit more expensive than competing options like YTTV, and wants to be perceived as a no-compromise premium cable TV service that happens to be delivered over the internet, then they shouldn't force their customers to use an antenna or separate apps to watch popular local stations that are typically included in cable/satellite TV packages. They need to carry the local ABC, CBS, NBC, Fox, PBS, CW and MyNetwork TV station in every market across the country, just as DTV satellite has done for years. And like DTV, they should carry a national feed of ION, plus a few of the retro diginets like MeTV, Get TV, Cozi TV, Comet, etc.