This is what is fundamentally missing from most talk about "tech" startups by VC types these days. They're not actually interested in the nerdy stuff, just in the "disruption" stuff.
L&S were, and they hired other people who were. They didn't start with a business idea, but with a technical one. They filled in the blanks on the business side after they survived the .com crash.
I didn't get to Google until 2011, but it became clear to me after joining that in the past they had gone on a very nerdy mission to hire all the nerdy people and collect them into one place to do nerdy things.
(Unfortunately that nerdy thing ended up being selling ads really efficient, but that's another story.)
My fundamental point is that the Google story is very unlike the kind of stories that YCombinator or a16z like. It started, like you said, as a set of intellectual/technical interests. The other stuff, that VCs today like, came later.
In a way they did the opposite of the usual advice. They started with the hammer (the tech) rather than the nail (the business problem.) They certainly didn't start with a "Like X but for Y" statement like seems to be desired by VC today. And they didn't look like the typical .com story at the time (which was usually: give us lots of VC $$ so we can sell something on the web that is currently not sold on the web, but we'll just use the $$ to buy customers and make no profit...)
I would posit that if today's Google came to YCombinator today they'd be shown the "no thanks" door.