I wouldn't say its meant to exclude. Black Lives matter is more about forcing people to include black lives into a privileged group that all other groups already belong to, namely a group that doesn't just randomly get murdered by cops because of their skin color.
Most people insisting that all lives matter know that all other lives have already been decided to matter and that only black lives are excluded from that list. As such its not an unreasonable reminder that black lives indeed matter.
I've never not been been under the impression that Black Lives Matter had a tacit "too" at the end, but this assertion is false.
If you look at police shootings in the US, the group that suffers the most from police violence is Amerindians, not African Americans. And even then, it's not "all other groups."
If you look at the baseline for police shootings, blacks, native americans, and Latinos are over-represented, while whites and Asians are under-represented. If anything, if you fall into the Asian group, you're less likely to be shot than a white person.
This is part of the reason I'm uneasy with BLM, and it's not because of the name. It's because the US has a problem with police shootings, period. Even accounting for its high population, the rates of deaths at the hands of police are absurdedly high - like, compared to countries in Europe, you're more likely to die at the hands of police by double digit factors. Of course, I can concede that some of it would be justified, because it's also got a gun violence problem, so where people are more likely to have guns, the police are more likely to use guns. But even so, the police do use firearms more readily than other countries. In the UK, off the top of my head, there's about 3 deaths at the hands of police per year, whereas in the US, it's around 1000. Even accounting for different populations, that's an insane difference.
And look, I'm open to the idea that a racialist approach will succeed where a universalist approach hasn't, but taking the former comes off as playing with fire. "All Lives Matter" is backfire effect in action.