Overall, my vote would be nay. To sum it up in a sentence, their product is not a medical device yet they are sort of trying to claim it is without saying anything they can't legally because of that non-designation. They claim x% injury reduction, better sleep, etc., but how? By what guideline? They say its the first such device backed by research, but as far as I can tell that means they selected a handful of scientific journal articles about related subjects (recovery, sleep, etc) to quote on their website that sound impressive, yet at the end of the day its just a very expensive heart rate monitor and sleep log that encourages users to use HR zone training and sleep more.
Improving your sleep, pushing yourself while avoiding overtraining, etc. -- are obviously good ways to improve as an athlete. My complaint is basically they're throwing the word 'analytics' around like its some sort of panacea. At the end of the day, did the device really make good recommendations that were specifically tailored for that user based on their data OR did the user get better because they had a daily sleep log that basically forced them to confront the fact that maybe they were sleeping 6 hours a night when they should have been sleeping 8. Going back to the fact that they're not a medical device with professional medical direction (i.e. staff MDs, NPs, PTs, etc. acting in an official sports medicine capacity), my gut reaction is 'no', this is a correlation does not imply causation situation.
Oddly enough, I saw a testimonial of theirs that basically proves the same point. It was someone saying how whoop was such a great thing for them as an amateur athlete who couldn't afford a coach to help them with their athletic development. Yet, what is a coach -- who is a human -- going to do. Are they going to run sleep analytics or are they going to have you write down how many hours of sleep you got/how you felt and either back off or ramp up training according to whatever qualitative information you give them? Are coaches saying 'man, you haven't been hitting your REM sleep targets this week, we gotta back off the mileage', or is it "coach, I feel really beat up and I'm not sleeping" "OK, take a rest day"?
As soon as you start measuring something in your life you're going to pay more attention to it. E.g., do you need a fancy expensive food tracking app or would simply starting to write down every bit of food you ate help you eat less junk food and lose weight? Yeah, the app would accomplish it, but so would the 5 cent piece of paper. It's the process that caused the change -- it's up to you to decide how much you want to spend for the tool to use in it.
I will readily admit that I am biased. Despite being an engineer, I feel like "analytics" has gotten to the point whre it's almost astrology for tech bros. Whoop seems like a fancy expensive toy for people that like gadgets. If that's you, by all means go for it. If not, start with the simple, almost free, approach and see if that helps before making any major spending decisions.