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.
The main thing you are missing is that what is put into the LC filter is not necessarily always a square wave. It is when the buck converter is in continuous mode, but unless you know that to always be the case, you can't assume the square wave input to the filter as you are.
In continuous mode, the output voltage is ideally the input voltage times the duty cycle. However, it's not that simple in the real world. Even if the input voltage stays constant, there is the DC resistance of the inductor to consider, the voltage across the switch, and the voltage across the diode from ground during the pulse low time.
The latter can be mitigated by synchronous rectification, but that isn't perfect either. At the least, there is the voltage drop across whatever is being used as the synchronous rectifier switch. Synchronous rectification timing is also usually made conservative, meaning it errs on the side of staying on a little too short rather than too long. The cost of turning off a little early is more voltage drop at the end of the flyback part of the pulse. However, the cost of turning on too late is shoot thru, which rapidly decreases efficiency, and risks damaging parts.
I have seen pre-regulation power supplies which were fixed duty cycle buck switchers. In one case, it was used to drop a 48 V distribution voltage down to a rough 12 V, which was distributed locally and dropped to the final regulated voltages by other power supplies. It didn't matter if the 12 V varied a bit.
A general purpose power supply has to be designed to handle low load too. Below some load for any switching frequency, a buck switcher can't maintain continuous mode. Some OEM supplies simply state a minimum load is required.
More general purpose supplies fall back to discontinuous mode. In that case your fixed square wave assumption fails. Now there are really 3 parts to the cycle. At the start, the input to the LC filter is actively driven high. When that stops, the flyback part begins, which drives the input actively low. Then there is the third phase in discontinuous mode where you consider the input effectively high impedance. The function of duty cycle to output voltage is not longer linear.
Best Answer
A quick search of Texas Instrument's products shows there are some 222 components between buck regulator controllers, integrated-switch converters, and fully-integrated modules that meet the requirements of 4.5-5.5 V in and 3.3 V regulated out. While there is some commonality between these components such as reuse of silicon dies in both converters and modules, it's fairly safe to say that there are over a hundred ASIC chips from just this one manufacturer that implement the control and sensing for a switching power converter. Yes, there is a market for these ASICs.
There are a wide array of power systems, starting with simple buck converters and going up to AC/DC supplies at kilowatts. You need to evaluate your design goals with perspective on the time/cost/complexity trade offs to achieve it, particularly if your end result is a salable product.
From my design experience, here are some reasons to use them over a custom-built solution:
The advantages of a fully custom solution include:
Overall, my recommendation: if this is a learning project, go ahead with it. Someone has to know how the inside of the system works and this may be a skill employers desire. If this is you needing 3.3 V at 2 A for something else, consider one of the ASIC options or even purchase an off-the-shelf buck converter circuit board.