I think the bike is the least important part of a pro team. The top-tier road bikes are all at the same level. I think the only significant variation is in TTs, where the bike, clothing and rider position as a whole really do make a difference. You can see that some pros and their teams pay more attention than others in this respect. TTs are also won and lost by seconds and there are no tactics other than riding as fast as you can. So a relatively small difference in bike performance could change the result.
Interesting analogy with F1. I was actually an F1 Race Engineer for 10 years (2000-2009) and there is obviously a much larger variation in car performance between teams. One thing that really stands out in F1 is tyre performance. Aero and power gains tend to find you time in tenths of a second per lap, where in a tyre test you could easily see 2 or 3 seconds of a difference between tyre compounds and construction. The Michelin vs Bridgestone tyre war in my F1 era was truly epic. We would literally turn up to a test with 50-60 sets of wheels and have a dozen sets of tyres sat in blankets ready to go. Tyre choice for a race was critical and that's where 95% of the effort went at the trackside. Back at the factory it was all about having the best wind-tunnel program and a reliable engine.
Relating tyre performance to bikes I would say tyres play a significant role in pro racing too. Nowhere near as critical as F1, but certainly a factor and almost certainly the most important bike component choice. I've heard Geraint Thomas talk in his Podcast about how he would avoid following the wheel of certain teams on wet alpine descents if he knew their tyres had poor grip.