Assuming the same head tube angle, why does my track bike handle
better with a short 38mm fork rake when on a smooth track oval, but
when set up as a road single speed it handles better with a 45mm
raked road fork?

A short raked bike has more trail and thus has better hands off
tracking when ridden on an ideal smooth surface. Photos of old time
track motorpacing show inward bent fork tubes (negative rake). I
thought this was to allow the bike to follow the pacer vehicle
closer, but it was probably to increase high speed stability via
increased trail.

Then why do road race bikes have more rake and road touring bikes
have more rake still? Why does my SS bike handle better on the road
with a 45mm road fork? Does this not decrease trail and
theoretically make steering less stable?

My theory is that the theoretical rake/trail diagram and a track bike
both assume an ideal smooth surface where trail is the main factor in
determining bike tracking and handling.

However, with a road bike, pavement imperfections come into play.
When a road bike front tires hits a bump or crack in the pavement, it
usually hits the tire more on one side than the other. The front
wheel gets deflected (slightly) and alters the steering (bump
steer). (Please note that I may be using the term "bump steer"
differently than the way it is used in the motorcycle and auto
industry). With a short raked track fork this deflection can act
through a longer lever arm (long trail) and exaggerate the bump steer
effect. Thus riding a bike with a track fork (short rake) will
feel "twitchy" on the road. But by installing a longer raked road
fork, the trail is decreased and the deflection has less leverage,
which results in decreased bump steer effect.

This is my theory explains why track bikes have short rakes and road
bikes have longer rakes. Therefore, when we convert a track bike to
road use, we should consider installing a longer raked road fork.

Am I thinking this out correctly, or is my theory hogwash?