Do induction cookers increase risk of cracking cast iron?
Cracking? No, not in my experience. I own like 20 cast iron skillets (I've been told I have a problem).

Warping? Yes. I have a 2,800 watt per burner commercial induction stove with a very small pattern like yours. If you repeatedly overheat a pan on high for searing, it will eventually bow outwards. Warping can be mitigated by preheating your pan gently.

That said, if the pan is full of water or oil (for deep frying, not stir fry) there is nothing to fear. I have had the same stainless stock pot for 8 years and I roast it on high all the time (with liquid). Water is a very effective coolant (it's what keeps your car engine from overheating). The likelihood that a pan full of water will overheat is very unlikely, nigh impossible.

RE: comments. Yes it is a lot of skillets. This is what 14 looks like.