EDIT: I made a bad simplification in my math, which made my numbers much worse. I would have failed that physics test. Oops. I've recalculated with what I hope is a less bad simplification, and updated the numbers. Super caps are actually closer to viable than I had initially guessed.
Based on your formatting I was trying to find the rhyme in you stanzas.
The short answer is that batteries (chemical storage) hold a LOT more energy than capacitors (electrical charge storage). And while super caps have really big numbers (Farads!) most of them still don't hold much energy (compared to a battery), and are either very large or have high internal resistance (so you can't get that energy out quickly).
Here is the very long answer:
Random numbers for discussion. What does it take to start a motorcycle? I'm going to say the battery needs to provide 50A for 5 seconds. I'll also assume that (using magic), the capacitor starts at 14V and ends at 10V during the starting event.
You can turn these numbers into total energy required.
Average Voltage: 12 V (lots of hand waving here)
Average Power: 600 W
Total Energy: 3000 W-s, or Joules
So we need 3000 J, and it's easy (
or not) to turn capacitance into Joules:
hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng.html
Example 1: A coke bottle electrolytic
This is a normal capacitor (not super), but the biggest I could find in stock at digikey.
www.digikey.com/en/products/detail/kemet/ALS70A135QT025/6928375
Size: 8.74" long and 3.5" dia.
Capacity: 1.3F
Using the numbers above (5V drop, 1.3F) I get 62.4 Joules in this big boy. If we had
48 of these on the bike, we'd be all set for one start.
Example 2: A regular old super cap
www.digikey.com/en/products/detail/tecat...BLS-7-5-16-2/9929761
Size: 3.1" x 2.4" x 0.5"
Capacity: 7.5F
So with this you get 360 Joules. You would need 9 of these to get just one start. Not too bad.
Example 3: A hoking super cap
That's not a super cap.... This is a super cap!
www.digikey.com/en/products/detail/eaton...R-16R2507-R/10461228
Size: 16.4" x 6.9" x 2.6"
Capacity: 500F
This time I get 24,000 J, which is actually a lot. That's enough energy for 8 starts. Cool. But it's bigger than the normal battery, costs $600, and will only hold that charge for 7 days due to internal self discharge.
The real answer is lithium batteries. For the same amount of stored energy, they are lighter, smaller, have less voltage drop under load, a higher cycle life, and a wider operating tamp range.
Of course, they also like to blow up, need complicated management electronics, and can't really be swapped directly into a 12V system.
On the other hand, lead-acid batteries are filled with acid which tends to eat the paint off of old KZs, which I personally am really sick of.
But if you're looking to move away from lead-acid, lithium is the direction you should look.
Personally I just buy
sealed AGM batteries, bring them inside in the winter, and from time to time put them on a Battery Tender trickle charger to keep them full. They last for years this way.