I left Google in 2009, quite unhappy about the difference between a startup and corporate politics. After that I worked at 3 startups (5 years), 1 telco (1 year) and at McKinsey (3 years).
I ended up interviewing at Google again in 2018, after deciding that a) I liked programming more than management consulting and b) my comparative advantage was in programming. I definitely could have felt entitled after 1) passing Google interviews once before, 2) having had three somewhat successful startups and 3) proving I can also handle the corporate side.
I was asked multiple questions that could be interpreted as 'algorithmic' (and I have to admit that after 3 years of not coding I was nervous about them). However, they can also be interpreted differently, more charitably. They all followed the structure of: 1) give a reasonable but not completely defined problem - you should be able to clarify enough of this to show you can deal with some ambiguity; 2) turn that into an algorithm - you should be able to articulate an easy algorithm and be able to discuss improvements to it; 3) turn your algorithm into code - you need to show you can actually program. I definitely didn't have to memorize and regurgitate textbook solutions.
I acknowledge that a) the above may optimize for rejecting all negatives at the cost of some false positives and b) it's still a very basic lower bar and doesn't predict who will perform highly vs. ok. However, I did think it tested for the core skills I expect from programmers.
I've also set up interviewing processes at startups. I did end up emphasizing ownership and 'getting things done' more than Google does. I do think startups should test for different attributes than 100k+ FTE corporations.