The company I work at is not a startup but we're small, and yeah hiring is hard. Being small, each person makes a huge impact. Someone who under-performs can be a significant net drag, not just in actual output but also in terms of opportunity cost. Fitting in with the team is paramount too as we can't shuffle people around, we're just a handful of folks.

So I can completely relate to wanting to be picky.

I'm not familiar with how things are normally done "over there", but here in Norway all the "how to write a job application" tips that the media writes about here every now an then includes some expert saying to go to the website, read what the company is about, read the job opening description carefully and write something relevant to that. Not unlike what you mention.