Many writers like them because they seem to have made both costly and cheap signals to show that they are on the side of writers:
(1) they say they are "anti-censorship" and won't evict writers from their "private platform"
(2) they let the writer own their audience / mailing list (so they can leave with their audience, if they want to)
(3) they advanced money to popular writers
These things with the addition of a simple writing/reading/subscription platform that isn't overrun with adverts gives writers confidence that substack is aligned with their interests and will make money while being on their side (this is true at least for now).
Additionally, the financial success of many writers on the platform has raised the status of creating a substack. I think this is an important secondary effect -- you can disparage this as "pseudo-intellectual" but there are people that are winning from it and doing well is always cool.
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*Edit*: Put another way, Substack's success is due to realism. They've made a realistic attempt to incentivize excellent writers to writing on their platform. They incentivize even those that are already very popular, by not locking them in and by giving them control of their audience. They have even gone as far as giving very significant upfront financial incentives to get the most famous writers on the internet onto their platform.
Other platforms try to own their writers and treat them like commodities producing SEO content. This was obviously not an attractive offer to talented or independent writers, let alone writers that have already grown huge audiences.