Indeed, what I said is very simple. The actual operation is much more complicated. Automatic frequency hopping can resist interference, but the jamming system can also follow FM. Modern jammers can counter high-speed frequency modulation, spread spectrum, code division multiple access, and sensor fusion. , Active and passive switching and other anti-jamming system capabilities
If FM was that easier, USAF would've figured that out by now. Yet, they still can't penetrate Syria properly. They have to tell the Russians that look we are going to bomb some sites, so you better off shut your jamming systems so that your batteries remain safe and our pilots get to reach home later. And so there are many discrepancies to your theory.
1. Consider a EA-18G, the jammer on the EA-18G Growler is the AN/ALQ-99 which operates on S-band. For an EA-18G to do a burn-through to an S400 battery (radar complex operates on S band but newer versions are rumored to use L-band as well) which include powerful radar complex, it has to be close to 70-90 miles to do that.
2. To facilitate more effective jamming, another approach is to fire an anti-radiation missiles such as HARM or MALD decoying system, which keeps the S400 radar complex busy. Which the USAF has well thought off, but again that has to be done in close proximity and for a considerable amount of time. A bait and fetch tactic requires half of EA-18G squadron to be performing the bait, while the other fire off these weapon packages but that also means, giving enemy your location as soon as you start on jamming. They all will be lit up like Christmas trees, so that is for sure that some pilots are not going to go home that day ever again.
3. The whole point of S400 battery is to provide another "layer of air space denial". So theoretically, you have to throw an entire squadron worth of EA-18G to do that, which is not going to scale properly in an actual battle, where they would be detected at 400Km to 500Km range by other batteries. Then they will have to split there jamming to incoming interceptor squadrons and air to ground jamming, so your whole "force multiplier" thing becomes less effective already.
4. USAF understood this, so they threw there AEW suite to F35, which can theoretically close in that gap and get near to an S400 battery. But now you are dealing with too few F35s. Think of this, why the rumored 6th gen fighter jet of USAF is based of an objective called Penetrating Counter Air (PCA).
5. Another school of thought is that to do an effective jamming, you require enough computational power and energy to continue that burn-through rate, which is difficult to perform in a hostile and contested airspace. Typically ground based radar complex have no issues with sizes and power output, so air-to-ground jamming is already discounted. HS-FM, Spread spectrum, code-division "multiplexing" looks cool in animation but is not that simple.
6. Engaging an enemy squadron of EA-18Gs can be thought of buying time, in S400s case, it also another means to keep the enemy busy, until the cavalry arrives. S400 was never thought of as "the force that can make pilots shit in there pants", but to keep a wall in front of enemy forces that will require a lot of time to do the jamming, and time is worst enemy for a fighter-pilot who was trained to shoot and scoot.