What are the reasons for this radial piston engine shut down procedure?
It could also be to remove lead deposits from the spark plugs. Some avgas has an agent added to remove lead deposits, this only works above a certain temperature which is achieved above a certain RPM. We had to do a similar procedure in the Cessna 152.

As you will know, Avgas 100LL contains a compound known as Tetra Ethyl
Lead (TEL) which acts as an octane booster for the fuel. This results
in a fuel which is commonly known as a 100 Octane lean mixture and 130
rich mixture Performance Number fuel.
In practice it is even better than this, with ratings more like 106
lean mixture &amp; 130 rich mixture which are far in excess of the
comparable 85 - 87 octane of road fuels. To achieve this a lot of TEL
is used - around 5 times the quantity that was used in the old Leaded
automotive fuels.
This increase in octane allows aviation engines to produce more power
through increased compression ratios or alternatively by increasing
the inlet pressure by using a turbo or a supercharger. The problem
with using Leaded fuels is that they will always burn with more
deposits than unleaded fuels.
The Tetra Ethyl Lead used for octane boost in the fuel naturally
degrades to form Lead Oxide when it is burned. In reality it is this
oxide which gives the octane boost. The problem is that Lead Oxide is
a solid up to about 900 deg C which is well within the wall
temperatures inside a piston engine.
In order to prevent these deposits from forming, a Lead scavenging
compound is added to Avgas 100LL - this compound is Ethylene
Dibromide. This scavenger is designed to react with the Lead oxide to
form Lead Bromide which is more volatile - becoming a gas at around
200 - 250 oC. This is a low enough temperature to ensure that the Lead
is removed from the engine as a gas end it subsequently goes back to
the solid phase as the exhaust gas cools in the atmosphere.
As a point of interest the pale brown / ash coloured staining that is
often seen leading from the exhausts of high powered engines, such as
those found on the warbirds, is in fact Lead Bromide.
To enable this reaction between the Lead Oxide and the scavenger to
work, there needs to be a relatively high combustion temperature.....

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