Max HR? Working this out accurately hurts! The generic formulae (220 – age, etc) can be way out. Yes – as a 56 year old who hits upper 170s/180 on a hard climb, I agree.
Very roughly Power ~ 2 x HR – 80, but HR lags behind effort when not at steady-state. Very roughly – otherwise you could never do a few minutes at 350W+
There is also thermal effects. – My body temperature has a BIG effect on my HR. At the start of the ride around 150+ HR is a big effort, once I am fully warmed up later in the ride the same effort will be 170+ HR.
I find HR is good for pushing hard on intervals (within 60-90sec you can see just how hard you are pushing), taking it easy on recovery in between, and also pacing on longer fast sections so you keep a sustainable but hard pace. This is especially helpful on exercise bikes.