“You would say”… this is what?
Sure, it looks like a chimney, what is it actually?
Fireplace chimney?
Appliance/Utility flue ‘chase’?
What is at the bottom of that ‘feature’?
Is it ‘Active’ or ‘Abandoned’?
Seems to me with an opening that large, there is gonna be a heck of a lot of rain/snow/ice going down that shaft!
Where does it wind up?
What is being affected by the moisture intrusion?
How is the water being controlled?
Lot’s of questions with no information.
A cricket is a non-issue. The flashing in place will handle any rainwater/snow melt just fine.
2" inches will make zero dfference with or without a cricket!
If you were a code inspector, then sure.
But as a Home Inspector the better question is “is it functioning”, “are there signs of leakage inside”, “why is the chimney cap missing”, “what is this single layer of brick thing anyway – why is the construction so insubstantial”, “why is the mortar cracked and is mortar even the right stuff”? And “what’s that pile of snot to the left for the plumbing penetration”.
Forget the cricket, unless you’re a City inspector with a rulebook.
If there is attic access then the condition of the roof sheathing viewed from the attic will tell you all you need. The older the house the more evidence you will have. New plywood around the chimney, existing water damage, pieces of old rotten plywood laying around from the last repair or water stains, new or old, on the ceiling at the fireplace will confirm how well the flashing has worked over the years. A well built cricket only needs a small flashing defect to leak. Many times you can’t see it standing on the roof much less from a drone.