The reason a weak battery/starter can't start an engine is because it can't push it through the compression stroke.
I agree with you there as I had previously mentioned somewhere back in this (soon to become) endless book of words, if my piston rings are well soaked in oil, the engine will start in 1/2 a rotation or less. And that's even when the engine is hovering around 0°C or 32°F. If the rings are relatively dry (even after cranking with the stop pulled out) it's grunt, grind, and groan until those rings are soaked in oil. As a matter of fact, somewhere in my horder's collection of 2GM20F operator and service manuals, I seem to remember a statement of using extreme caution when rotating the engine by hand in that the decompression levers are open to avoid accidental starting.
But I'm not really interested in pissing contest.
Well, I would but I've already had my morning leak and I don't have the capacity to get into a match now, other than to say that if you can roll over that compression stroke quickly and your rings are wet, it's off to the races NOW.
Next time you have absolutely nothing better to do, check your compression by hand (with a slack V belt) after it hasn't run for a couple of weeks. It's slow but you can get it past the compression stoke. Now fire up your engine for about 5 seconds and shut it down. Leave teh engine to cool down for a half hour to ensure it's back to ambient temperature and try the poor man's compression test again. You will have real problems getting it over the compression stroke with the rings still wet. If it's still relatively easy, you've likely got leaky valves.
Food for thought.