SEO folks, does it make sense to build the pages around low volume and very high intent keywords?

Maybe, it depends (as always with SEO). It can be successful as this case study shows: https://flyingcatmarketing.com/case-study/trevor-io/ I’m also using a low-volume keyword strategy for a side project of mine (new domain), and it’s working.

Yes. Absolutely. 💯 Keyword research tools have a high error margin. What is reported as low volume might not be that low at all. Also there might be a lot of variations to that keyword you can rank for with that same page. Those add up. Also, if you’re not writing about the high intent stuff, how is your website supposed to sell anything?

If it has high purchase intent, it’s generally a good idea to show up in search for it.

Yes, especially for bigger deal sizes. We had a page at the last company I was at that had maybe 100 visitors a month, but it got 20 solid leads/month because it was a pretty niche offering

Yes, I've seen startups use that strategy before. Like the other posters said, the tools have limited information.

I think you should start with low volume keywords with low keyword difficulty. It is easier to rank for low volume keywords with your current DA, but targeting high intent keywords is uncertain.