I think a steep seat tube allows a shorter wheelbase.

My Pista has a 75 and 75 head tube and seat tube, for a short wheelbase and quick handling.

My Karate Monkey has somewhere around 73 and 73, but the seat tube has a bend in it that may not shorten the wheelbase as much as it allows me to put more weight on the rear wheel and less weight on the front wheel.

Let's see then: one could say four main factors determine handling, or one could say only three factors determine the quality or nature of the handling, with other secondary, contributing factors.

But let's look at the three/four:

1. wheelbase;

2. head tube angle;

3. rake; and,

4. head tube angle and rake combined, or, trail.

Let's look at head tube angle, first.

A steeper head tube angle contributes to more immediate and linear steering response.
With a vertical, or 90 degree head tube, the steering responds directly in proportion to how much the rider turns the steering tube.

With a more inclined head tube angle, the steering responds slowly, at first, and then responds much quicker as the rider turns the steering tube, until the amount of steering seems greater than one would expect.

One can see this better if he exaggerates it, as on the chopper motorcycles with dramatically extended forks and very, very relaxed head tube angles.
When one turns the steering tube on one of these motorcycles, at first, the motorcycle hardly responds at all, seeming to have very slow handling.
However, at a certain amount of steering tube turning, the wheel begins to lay flatter on its side, and steer off at a greater angle.
The steering response increases at a greater rate than one would expect from the amount the rider has turned the steering tube; and we describe this as non-linear.

So, a steep head tube has quicker initial steering, but it remains relatively linear and does not increase out of proportion to the amount one turns the steering tube.
Conversely, a relaxed head tube has slower initial steering, which increases out of proportion to the amount the rider turns the steering tube.

Secondly, we have rake.
Rake defines the distance of the axle, either in front of, right on, or behind a line passing through the center of the head tube and extending to the ground.

But let's talk about this head tube line for a minute.

A 75 degree head tube has a 75 degree line passing through it to the ground, in front of the bike.
A 90 degree head tube would have a line straight up and down passing through the head tube, and that line would intersect the ground directly underneath the head tube.
Taking it to absurdity, a zero degree head tube would lay perfectly flat, and a line passing through a zero degree head tube would parallel the ground and never intersect the ground.

Most bicycle forks have a forward curve to them that places the axle in front of the line passing through the head tube to the ground.
A shopping cart has the axle of its front wheels behind the line passing through the head tube to the ground.
A bicycle has its axle in front of the line passing through the head tube to the ground.

Now, drop a plumbline from the axle to the ground.
On a bicycle, this plumbline intersects the ground behind the point where the head tube line intersects the ground.
Remember, bicycles have less than a 90 degree head tube angle, and this places the head tube line and the wheel out in front of the bicycle.
In fact, the head tube line intersects the ground in front of the front wheel.
The plumbline hanging from the axle and intersecting the ground, and which also signifies the point at which the tire contacts the ground, generally, this axle plumbline intersects the ground behind the head tube line.

We call the distance from where the head tube line intersects the ground, to where the axle plumbline intersects the ground, the "trail," because, the tire contact point "trails" behind the head tube line and ground intersection.

Most street bikes have a rake of about 38 to 43 millimeters, which places the axle 38 to 43 millimeters in front of the head tube line.
The greater the rake, or the further we place the axle in front of the head tube line, the less the tire contact point trails behind the head tube line and ground intersection.
The shorter the rake, the less we place the axle in front of the head tube line, and the less closer the tire contact point gets to the head tube line and ground intersection.
In other words, the shorter the rake, the greater the trail.
The greater the trail, the more the steering acts like a shopping cart wheel.

So, track bikes typically have steep head tube angles and a short rake, which means quick initial steering, but, because of the long trail associated with a short rake, track bikes also have greater stability.
So, track bikes have quickness combined with stability, which sounds good, but also doesn't make much sense.
Quickness of steering would seem to work against stability.

Hm.

Well, it does work against stability.

Track bikes do not attain the speeds that road bikes attain.
I think it fair to say track bikes live below 35 miles per hour.
At higher speeds, such as a fast racing downhill where bikes hit 50 and 60 miles per hour, a track bike would get into "high speed wobble."
High speed wobble takes me beyond my level of understanding, and so I can't say why it happens more with a bike set up for the track, but it does.
Conversely, road bikes, which, to me, have relatively dead handling, do very well at racing speeds.

In other words, designers can tailor the geometry of the bike, meaning, wheelbase length, head tube angle and rake (which together determine trail), for a given speed range.

My Bianchi Pista has the steepest head tube (75 degrees) and the shortest rake (28mm) of any bike known to me.
It handles very well at the street speeds where I live, below 20 miles per hour.
In fact, at 20 miles per hour and below, I can't imagine it getting any better than a Bianchi Pista.

In comparison, a Mercian Super Vigorelli, a real track bike, has a head tube angle of 74 degrees and a rake of 33mm; which means, the Mercian folks designed this bike for more competitive, higher track speeds than the typical Bianchi Pista rider will ever see.

If a person wants to ride a fixed gear with a big chain ring and a small cog on the street, and go very fast, he might want a frameset with a more relaxed head tube angle and a longer rake than one would find on a Bianchi Pista.

I've ridden my Bianchi with a big chain ring and a small cog, at 82 gear inches, and I can do it and the bike can do it, but the bike doesn't feel good doing it.

I like zipping around town, with lots of acceleration and deceleration, shortcuts and precise handling at slow speeds, and the Bianchi Pista works great for me at my present low, low gearing of 59 gear inches.
I never go very fast, as much as I go quickly.

So, in what speed range does a rider want his bike to excel?

Slower?
Then the rider wants a steeper head tube, shorter rake, and shorter wheelbase.

Faster?
Then the rider wants a more relaxed head tube, a longer rake, and a relatively longer wheelbase.

Or something in between...