You absolutely need to do this unless you're in crazy demand. Every generic resume I've sent out has yielded exactly zero phone calls. Every tailor-made resume I've sent out has gotten at least to the in-person interview stage.
Survivor bias? Maybe, but 5 jobs in since college and I'm never sending generic resumes anywhere ever again.
I did find that when I was applying to the bigger SV companies (and Seattle), I wasn't necessarily applying for a specific position, so even if I had wanted to tailor it, it would have been more of a challenge. That's just my experience though. I do believe that if I was going for a very specific position, I would definitely spend the extra time to make sure it was perfect.
I'm sure if I was trying to get a job at Buffer or someplace like that where you are mostly applying to the company, I'd need to rethink my strategy.
(I have no affiliation with Buffer whatsoever).