I’d suggest more specialization to reflect that some domains have materially different execution models, evolutionary timelines, and product playbooks when done optimally. There is some of this but it feels like there is often a tacit default model that every startup is social media, simple SaaS business, or similar and is biased toward what works in those domains. There are VCs that specialize in less conventional startup domains but the accelerators that teach people how to quickly and effectively execute some of these domains are limited when generic startup advice no longer applies.

If you are doing hardcore data infrastructure software, some kinds of defense tech, et al the startup building process is sufficiently different that first-time founders would benefit immensely from accelerators that really understand from direct experience what those startups need to do to be successful.

I'd say the only real reasons any founder needs "accelerator"/any kind of VC firm is lack of money and/or domain-specific professional help/mentoring when encountering a problem that seems to be too hard to overcome by yourself.

So, ideal accelerator/VC would be one that would want to fund your (ad)venture without taking too much motivation off by having large ownership/control, and have connections/pool of domain-specific professional expertise. And wants to believe in you.