Almost all cyclists who ride road bikes set the seat so high, and when they're in the drops their body can be almost parallel with the road, reducing air resistance. However,their legs can't reach the road from the saddle, and their head is pushed down and it could be dangerous in some situations. With a low saddle position, I feel comfortable and can easily reach the road from the saddle, and my head is upright. When I want to be more aerodynamic, I can drop my upper body and push my rear behind the seat. So why don't cyclists use a low position seat?
Road cycling position is generally a performance position (although not always) and can be viewed as a compromise between three components:
- Power - different positions will allow you to output differing levels of power depending on your biomechanics.
- Aerodynamics - some body positions reduce your power, but can reduce drag even more therefore allowing for higher speeds.
- Comfort - The position needs to be sustainable for long periods of time.
Depending on your goals you tend to weigh one category more heavily. For example, endurance riding tends to be more upright which prioritized (3) at the cost of (2).
Saddle height tends to have the biggest impact on (1). Too low and you do not use all of the power stroke of the quadricepts, too high and you start leaving the power stroke and can over extend your hip and knee. The most powerful and efficient saddle height leaves a small bend in the knee at the end of the pedal stroke. This lets you use your quadriceps to the end of their power stroke without over extending. You will not be able to reach the ground easily while remaining on the saddle.
Therefore to answer your question:
When I want to be more aerodynamic, I can drop my upper body and push my rear behind the seat. So why don't cyclists use a low position seat?
You may be able to change body position to maximize aerodynamics (2) but you are still sacrificing power (1) and will be going slower than someone who first maximizes power (1) then gets as aerodynamic as possible. Finally, a low saddle position can affect hip flexion (making your hips and knees flex more) which can be further affected when getting the body into a lower position, therefore you could also be affecting comfort (3) which makes the position unsustainable in the long run.
You usually spend much more time cycling along the road than stationary on your bike with your feet on the ground. Given that, it makes sense to sit in a position that makes cycling work better, as long as it doesn't make it too difficult to stop.
The standard recommendation for saddle height is that your leg should be almost straight with your heel on the pedal in its lowest position. That way, when you pedal with the balls of your feet, your leg is slightly bent at the bottom of each stroke. This is the most efficient way to pedal; pedaling with a bigger bend to your knee means you need to exert more force with your butt muscles, and transmit more force through your knees. That requires more effort and can cause injuries. It makes going up hills much harder.
With your saddle at the right height, you should still be able to reach the ground with the toes of either foot, but probably not both at the same time. You might need to lean the bike over slightly, but probably not much. That's all you need to be stable when you stop. If you're going to be stopped for a longer time you can always get off the saddle and stand in front of it, straddling the crossbar, with one foot flat on the ground and the other on the pedal. If you find that you can't comfortably reach the ground with the saddle at the optimum height for pedaling, you can always lower it a little.
Note that you don't need to be super-aero just because your saddle's at the correct height. You can always raise your handlebars so you can cycle more comfortably.
First, because in your position it takes effort to pedal standing up instead of sitting, and that effort is better spent in moving the bike forward. Maintaining one's weight at back takes more effort than the usual standing pedaling position.
Second, because there is no need to reach the ground with both feet while riding. When stopped, it is easy to get out of saddle, tilt the bike enough to reach the ground or just reach the ground with one's toes. Most people have moving joints in their necks and can turn their heads so that they can see.
The only time I've felt the need to take saddle-to-ground distance into account is riding with a high weight (toddler seat), when tilting the bike so you can reach the ground doesn't really work. Even then it's toes only on the ground or stand over the top tube. The saddle is only about 1cm or 1/2" lower than for distance in that case.
None of that applies if you're racing.
On closed roads in a peloton you don't have to pay attention to the same things as normal riding. And you're so close to the other bikes you don't have good visibility anyway. So the head down isn't too bad either. Besides, with practice you can ride for hours with your head tipped back. And at race speeds and conditions you're unlikely to have to put your foot down in a hurry - if it's not a planned stop it's likely to be a crash whatever your riding position.
An important point is the forces placed on the knees. The lower the seat, the more acute the angle of the knee is when force is being applied to the pedal. This results in an unnatural stress on the knees which can lead to patellofemoral syndrome and patellar tendonitis, among other conditions.
Of course, over-extending the knee due to a seat position that is too high can also cause problems.