I'm not sure that the labels themselves are the issue in either of these cases. It's worth remembering that we're talking about historical periods of mistreatment as well. From my experience, Psychiatry as a whole has historically had its favorite diagnosis for the 'bad and unwanted' people in society. Hysteria is the obvious reference, but that shifted towards labeling the 'undesirables' as schizophrenics (and later as borderlines). It wasn't (and in the case of BPD, still isn't) uncommon for people to receive these labels purely to communicate to other doctors "I don't like this patient"/"They're faking"/"They deserve mistreatment".

Let's not forget that the label of schizophrenia started as a combination of the idea of early-onset dementia and stigmatization of behaviors that do not fit into society. The latter half is covered up by history, but the initial 'symptoms' of a schizophrenia diagnosis included things like not making small talk and having strong beliefs about politics. The list of symptoms read half of what you'd expect in terms of psychosis, and half like it was copy-pasted from the 'symptoms' of Hysteria. That's why these additional labels were harmful - some of them were associated more with not fitting into society than actual pathology.

It's no coincidence that when this general issue of mistreatment and over-diagnosis was being fought against, Psychiatry was busy switching over to using Borderline as the new maligned diagnosis. The schizophrenia labels were removed during the wider push for humanizing treatment of schizophrenics, but I don't think the labels themselves were a significant part of the issue - the bigger issue was the inherent power imbalances and patient abuse present within Psychiatry. After all, BPD was previously unnoteworthy, but now has become the new stigmatizing label, and all the mistreatments of schizophrenics are being shifted to borderlines. After all, there's now a "quiet borderline" label - for people who clearly aren't borderline, but psychiatrists want to give the 'bad diagnosis' to anyway.

Autism is adjacent to Psychiatry, but the story is the same. Autism is currently maligned by society, and the fact that people are so hostile towards autistic people is the real problem, not the labels they've made up to 'justify' their hostility. Getting rid of the labels doesn't remove the hostility, because the hostility is just looking for an outlet. That's why my only focus is making sure that labels are medically useful - because managing societal and medicalized hate of disabled people is another issue altogether.