Vertical BJT current flow direction

In a vertical BJT, why does the current flow vertically downward?

So the base surrounds the emitter, and the collector surrounds the base. Eventually the current will flow into the collector ohmic contact at the top. So why doesn't the current flow laterally towards the collector terminal? From what I read in textbooks, it takes the long way of going down vertically and then move its way across and up to the collector terminal. Being that we bias the base/collector/emitter at the top, then the strongest voltage would be at the top. And since we surround the emitter with base, and surround the base with collector, it seems current should be able to flow any direction, so why not take the shortest path and go straight across.

In an IC technology the current flow is "mostly" vertical
through the base, owing to the difference between base
width (Z dimension) and base-overlap-of-emitter (X, Y).
In the collector it is more of a 3D problem and depends
a lot on the subcollector / sinker (or lack) construction.
A good low resistance sinker and buried layer will make
most of the voltage gradient (hence current flow)
vertical.

The lowest resistance electrical path is not necessarily
(and especially if engineered) the shortest distance.

And of course with a discrete device type construction
where the collector contact is on the backside, there
is really no choice for the current.

When we modified medium voltage linear bipolar flows
for purposes like regulators and PWMs, adding the
better (but more expensive) collector features was
most of the difference.

If you take a look at the doping profile and base layer thickness, you'll realize that lateral current flow doesn't play an effective role by the large base resistance. Due to the long lateral base path, it's current gain is also rather low.