Honda is using a Li-ion battery (12V, 4.5Ah, 80 CCA) for their premium vehicles like Honda CBR1000RR Fireblade SP and Honda CBR1000RR Fireblade SP2.
The capacity (indicated in Ah) isn't that important. A battery's ability to start a car is indicated as CCA (cold cranking Ampere), i.e. the maximum current a battery can supply for 30 seconds.
A 1 kW starter motor (pretty big for a bike engine) draws 80 A, that times 30 seconds is only 0.7 Ah. So a 4.5 Ah battery can start the bike several times. These motorbike battteries have CCA values in the region of 80-150.
Yes, it is perfectly useful for starting a 1000cc engine. For example, consider the Omega Mechanix IJS-6000D jump start kit: https://www.amazon.co.uk/Omega-Mechanix-IJS6000D-Intelligent-Charger/dp/B00YWU4RM6
It is only 6000 mAh = 6 Ah. It can start a gasoline engine up to 5 liters in size.
So, if you scale this down, 4.5 Ah battery should be able to start 3750cc engine. Your tiny 1000cc engine is nowhere close to this.
The reason the batteries are typically larger than this is that you cannot run the electrical loads such as lights with the engine turned off for any useful length of time using such small batteries. Also, batteries degrade as they age, so even if a 6 Ah battery will start a 5000cc engine when new, it may have difficulty doing that for ten years multiple times per day. But considering that 4.5 Ah will start 3750cc engine, and that the engine is only 1000cc in size, there is a huge safety margin that will ensure the system will continue to work even as the battery degrades.