Fast Eddie said:I picked up on your point that: ' It really makes no difference whether it is a heavy flywheel or a heavy rear wheel that adds mass to the system since any component subject to angular acceleration (shafts, gears, hubs, rims, etc) affects the system in the same way'.
Now, I'm not gonna do your water tyre experiment! But many modern bike mags have agreed on the results of fitting lighter carbon fibre wheels to bikes and all note, state, record faster acceleration as a result.
Absolutely, lighter wheels can make a significant difference. I experienced this first hand decades ago when my brother had a vintage European 10 speed bicycle with steel wheels and utility tires on it. He fit alloy wheels and some light tires and it was startling how fast you could accelerate and how responsive the bike was after the wheel/tire change. Totally transformed the bike.