You are not hitting your max. Sure, you are up there and anaerobic and feeling crappy, but those exercises will not put you at your max. The formulas are a guide, but basically it boils down to genetics. You need to do a stress test (best if you get professionals to help you) where you are put to the max and your heart rate eventually peaks where you feel like you're going to die, but it won't climb any higher. You can guesstimate that your max HR is probably not too much higher than when you feel horrible during these workouts, but you are very likely not at your max under these conditions. Whether the number is relatively high or low compared to the formulas has no indication about how fit you are. Mine is pretty high. That just means that my comfortable working HR is also pretty high compared to others my age. That doesn't mean I'm fitter or they are. Resting HR and recovery time are better indications of cardiovascular fitness.

HR recovery time is another story altogether. When you get up to 80% or more, the time it takes your HR to get back to a moderate level indicates how fit you are. The more fit, the faster it will recover. So eventually you'll be riding your bike pretty hard at 185bpm, hit a red light, and in a minute of rest your HR will be down to, say 100bpm.

Interval training does the most to improve recovery time. You start out with long periods of recovery between short periods of hard work. Eventually, you shorten the recovery periods. Finally, you actually do recover in short periods of recovery. Just improving overall fitness will also help your recovery time, and it may also lower your HR for a certain perceived exertion rate.