Why doesn't it?
Because autistic people haven't set up the same kind of community for the same reasons, with the same history.
You gotta understand that LGBTQ+ isn't even that old as a term. I'm 50, and I was damn near an adult before LGB was an initialism that you'd see often. Tbh, you only really saw it at pride functions, rights functions, and very rarely in LGB media. The T being added in is what? Maybe fifteen years old? It's hard to remember when trans issues became unified on a large scale with gay issues (using gay as a catchall term here, not an exclusion; back in the day it was very often lumped under that term for whatever reason), but I know it wasn't fully integrated in the early 2ks, since I was still able bodied and interacting regularly with rights activists. It was getting there, but the T wasn't added across the board yet.
The Q and other additions are even more recent.
Autism as something other than an illness that needs management is pretty similarly new to the public consciousness. So autistic people didn't have the same kind of community of exclusion the way LGBTQ+ people did. They were patients, not minorities.
That may seem like sophistry, but if you look at aspergers, there was a community, it just wasn't one of exclusion in the same way. That community had a lot more similarities to little people (dwarfs) than gay people in terms of how each group interacted with Neuro or physical typicality. There's definitely a lot of prejudice, and condescension and bullshit involved with being autistic or a little person, but it's not the same as being actively hated and even killed for being born as you are.
So LGB people came from a place where community was safety in a way that someone with autism doesn't experience. Trans people do too. As do queer and "other" groups distinguished by sexual orientation or gender.
Safety in numbers was literal safety.
The political and social side of banding together was essential to that safety. Every "letter" added means more people working for equality and fairness. Every "letter" means more voters, more money, more influence.
Autism, on the other hand, hasn't needed that yet. So far, all the various aspects of autism can be addressed as a group despite the various aspects of its expression the sensory sensitivity group and the focus related group are part of the same spectrum, that can be easily navigated by social and political efforts as a single group by default.
Lesbians, gay men, and bisexuals aren't the same spectrum. The lived experience of each group (and for bi men and women separately) isn't inherently linked to the others. Sexual orientation may be a spectrum, but it has different social and political ramifications for each version (and the versions that came into aw areness later). Pointing at a lesbian and a gay man and saying "those are the same thing" makes a lot less sense on a social level.
This isn't to say the lived experience of autistic men and women is the same, it most definitely isn't. But both of those groups can benefit from the same efforts in a way that lesbians and gay men couldn't until they banded together more.
Now, should there be delineation between the different presentations of autism the way your post suggests? Not for me to say. I'm not involved in enough autism groups to have knowledge of whether or not the greater community would benefit from it. And, being an outsider, there's limits to how much I can pick up from observation compared to someone that's living with autism. There may be a very pressing need to split the categories of autism so that social and political efforts can be improved.
But that's a separate issue from why it hasn't already developed such a system.