I'm sorry, but you are demonstrating quite clearly you have no idea what is it you are talking about. I do not know of any missile guidance which uses FMCW, though I do not discount the possibility that there are some which might use it. However, the vast majority uses CW and not FMCW, like the SARH Sparrow II, the ESSM etc.
From what I know, the Nike Hercules, the S-200, uses it, as well as most SAM radars, which by the way, do need range information on the tracking unit. Often the term is Interrupted CWI. Aircraft radar also uses, starting from the earliest sets of the F-14 and the F-15.
ESSM uses it under the term Interrupted CWI.
Another system that uses it.
So does the Standards.
Aircraft system that uses it.
The term FMCW, FMICW or just ICW is used interchangeably but mean the same thing.
They get range by using the phase modulation technique, not frequency modulation as in FMCW. The search or target designation radar is not the one which uses CW, it is the target illumination radar, if SARH guidance is used.
How so? Phase modulation isn't as widely used.
I'm sorry, your basics here is so far gone I truly don't know where to start. I can only try to correct some parts but the basics you'll have to really pick up a textbook to understand. Chirps are not 'peaks', (whatever you mean by 'peaks'), they are signal changes in freq over time. It is not 'peaks' but peak power transmitted that is what ESMs utilise for detection.
They are frequency changes over time to be exact. Like sudden increases in frequency and these bursts of short frequency create compressed pulses. FMCW does not offer any decrease in terms of peak power over CW.
FMCW allows for reduction in peak power transmitted while still maintaining (as best as possible) average power transmitted. That's why FMCW radars like Scout can have low peak power outputs on the order of 1Q or below. Average power transmitted is the parameter which determines radar detection performance. To make it simpler for you to understand, what FMCW accomplishes is to make the transmitted peak signal so weak the ESM cannot pick it up. If peak power reduction doesn't constitute a legitimate LPI technique in your eyes, I don't know what can. I do know that radar engineers agree with me on this though.
Excuse me but FMCW is used in a much broader term. It just seems to me that you just discovered FMCW newly with the context of LPI, when in fact, FMCW has been around nearly as long as CW is around, which was before Pulse Doppler. FMCW is simply, a way of getting range for CW.
FMCW can be used for LPI yes, but not all FMCW radars are intended to be LPI.
Scout uses FMCW not primarily as an LPI form, though the bonus is convenient, but for use as short range radars, FMCW does not have a minimum range like pulse doppler, gets less ambiguities, it works better at short range, resistant to ground clutter and therefore better to detect and track low flying objects. That's precisely why its used (in different terminologies) in most SAM systems.