Why do we clock Buck Converters?

There are lots of hysteric or modified hysteric buck converters available. For example take a look at TI's DCAP constant-on time converters:

TPS53355

Or a more conventional true hysteric buck converter:

LM3485

Hysteric buck converters actually require some minimum ESR in the output caps for stability, so they tend not to work well with ceramic output capacitors. (Without some modification.)

Also in a true hysteric converter (not as much with the COT approach) the switching frequency isn't constant. This can be a problem at light load when the switching frequency may get down into the audio band causing audible whine or noise. It may also cause interference with other circuitry at certain frequencies.

Because of that it's also difficult to filter conducted noise.

Yes, I've actually done that. It's a bit tricky to design, because you have to very carefully compute the currents, voltage changes, and reaction times of the comparator. To keep the variations down, such designs are usually for limited input voltage range and a fixed output voltage.

What you describe is really one form of a pulse-on-demand system, in this case implemented with analog electronics. Pulse on demand has more ripple than something that controls the PWM duty cycle to regulate the output. However, they are simple, inherently stable, easy to analyze, and easy to implement in firmware.

I sometimes use a PIC10F202 with a pulse-on-demand algorithm as a low cost buck converter with a lot of forgiveness. In many applications 50 or 100 mV of ripple is fine. This is especially true when the buck switcher is a pre-regulator feeding an LDO at just above its minimum input voltage. One trick I use a lot with this kind of buck switcher is to use a PNP transistor around the LDO as a comparator to determine when the input is one junction drop above the output. That gives the LDO enough to work with reliably, but not so much to waste a lot of efficiency.

It's often convenient to have a +700 mV rough supply around. You can use it to feed distributed-point-of-use LDOs, and to power things that don't need a highly regulated voltage, like LEDs for example. This keeps the current demand off the LDOs, so they can be small and cheap, like SOT-23 or SOT-89 packages.

Such a converter is possible, but its output ripple will have very different characteristics from a clocked converter.

With a normal clocked converter the output ripple will stay at pretty much the same frequency over a wide range of loads, but will get larger in magnitude at higher load.

With your output voltage based converter the magnitude of the output ripple will stay about the same regardless of load, but the frequency of that ripple will be determined by the load. High frequency ripple is generally much easier to filter out than low frequency.

You also need to consider overshoot, especially at initial power-up. Remember in a buck when the switch is on you are charging the inductor. After you turn the switch off the voltage will continue to rise until the rate of discharge of the inductor falls below the current drawn by the load.