I have a high maximum heart rate; about 195 for cycling, 205 for running, and perhaps an even higher max for kettlebells.

Cycling has a lower heart rate for three reasons (none of which has to do with weight bearing!) -- in order of importance*.
1. Fewer muscles used -- mostly leg muscles, little active upper body motion.
2. Position of body relative to heart -- easier to pump blood to upper body, which is at 45 degrees or greater, so not pumping directly against gravity
3. Better cooling at faster mph -- a lot of blood pumping capacity can go to dumping core heat.

If you even sit up straight while on a trainer (no other upper body motion), heartbeat raises 2-3 beats per minute... Your heart rate will also be higher on a climb, especially when out of the saddle and actively using upper body (even more if cooling drops from a speed drop) -- you will be closer to your "running MHR" and not necessarily over your lactate threshold.

*for the triathletes -- swimming MHR can be 10-15 beats/min lower than biking...
1. Smaller muscles used, arms and upper body, which require less oxygen.
2. Body perpendicular to gravity, so easier to pump blood.
3. Excellent cooling from water, little blood capacity needed for cooling.

MHR is genetic at birth, but declines with age based primarily on how sedentary / active the person is. A competitive athlete might see no drop in MHR with age, while sedentary people have a drop of about 2/3 of a beat per year. (This is a compilation of the most recent studies; the first study that was done had many flaws I won't go into, but it spawned the ubiquitous 220-age "MHR formula" that will never die... this formula has a drop of 1 beat per year.)

The real reason to know your maximum heart rate is knowing when different energy systems are used. The lactate threshold is about 75-85% MHR, depending on training - this describes a particular blood concentration of lactate, but effectively is about when half of the energy is produced aerobically and half anaerobically. Knowing your lactate threshold is important for setting race / distance pace, tempo pace (faster but sub-lactate threshold) and for training to raise the lactate threshold. It seems like a lot of cyclists don't want to go above the lactate threshold... however, lactic acid / lactate is a fuel that your body will process better with increased training. It is *not* lactic acid buildup that makes muscles sore, it is excess H+ / hydrogen atoms from processing the lactic acid into ATP / fuel. As the body becomes more efficient above the lactate threshold, it also becomes more efficient at removing H+ ions.... I definitely exceed my lactate threshold on some short steep grades here, but my muscles don't get sore. (I think strength training really helped with using lactate effectively, since weights are anaerobic).

Exercise Science is kind of a hobby for me...

Oops, well on topic I just naturally spin at about 80-90 rpm on my road bike... What I do is spin up in a lower gear, then if I feel like I can apply more power I upshift, and keep doing this until my cadence starts dropping. The upshifting is new, which is exciting because I must be getting stronger!