You remember Jiminy Cricket? He was Pinocchio's friend, and a metaphor for his conscience.
I never saw him on a roof.
Depending on how a chimney is positioned on a roof, and how wide it is, a chimney cricket is the way to go.
On a wide chimney, wider than 30"or so, and a steep slope, a cricket really is essential.
So when I did not see a cricket behind this chimney, of course I recommended one.
INSTALLING ONE HERE WOULD CERTAINLY BE A BEST PRACTICE.
Another problem here is that the flashing is very short.
When water cascades down a roof slope, it will gain speed. Eventually, if there is a chimney there, it will crash into the chimney's backside.
Tall flashing can sometimes control its force. But a low flashing makes the interior very vulnerable to moisture migration.
Since this chimney is so vulnerable I recommended the cricket.
What's a chimney cricket?
It is a simple, angled, smaller roof behind the chimney, intended to divert water around it rather than into it.
So, why is this water diverter called a CRICKET?
There is much debate and speculation!
This roofing addition is also called SADDLE FLASHING.
The word "cricket" happens to be a Scottish slang word for "saddle."
At the outset of the chimney sweep industry in England and Scotland, young boys were often employed in the trade.
Taken from the local parishes and orphanages, boys as young as 7 years of age were taken in by tradesmen to work in and learn their trade. Being small these boys were perfect candidates for getting into and cleaning chimney flues. Plucking them from orphanages was very popular among chimney sweeps.
It was a dangerous and dirty occupation. Worked mercilessly, these boys sometimes died, choking from the inhalation of soot, falling inside the flues or getting stuck beyond the ability to be extracted. It was not until 1864 that legislation was passed to protect them and punish offending tradesmen.
I can see young boys calling that roof diverter a cricket, and riding it like a horse's saddle. That's my two cents.
My recommendation: if you notice a wide chimney without a cricket, see about getting one installed! It is easy to do and solves any future water problem behind the chimney. Be sure you suggest a CHIMNEY cricket though, and not confuse people with JIMINY Cricket.