I think it squelches itself because the C-Stick was programmed by backwards apes who thought it would be a good idea to assign its functions to a directional input + A macro instead of just straight up assigning them functions. Spamming it can cause the macro inputs to make weird stuff happen in my experience, usually eventually stopping outright by way of squelching. I'm not entirely sure of the squelching is intentional to discourage spamming, but the macros definitely do cause problems.. namely in online where lag is notorious for eating your inputs.
There's not a whole hell of a lot you can do about it besides getting used to the timing and mechanics of it all. I would also get very intimate with move buffering as it's one of the only consistent ways to deal with C-Stick shenanigans from Hal/Nintendo in Smash 4 and 5. Keep in mind move buffering has also been tweaked going from 4 to Ultimate, so research and practice is a must.
In terms of -when- and -where-, C-Stick for me is almost entirely reserved for aerials. I have it set to tilts, as does 99% of the population, and when using it for aerials it does a lot to help. First of all, macro or not, use of the c-stick is both the directional input AND the attack, so it all goes down with one input (on the controller end, the macro wiffs this up on the game end but here it's irrelevant) and that's obviously nice, but the big thing is momentum. Using aerials via the L-Stick + A is going to cause not only the aerial to come out, but it's going to make you move into the direction of the aerial. This can be hindered to an extent by letting go of the stick the second you input the aerial.. but not completely avoided outright. This can REALLY jank up your spacing, so using the C-Stick for spaced aerials is basically a must.. it's also practically a must for proper retreating aerials and good RAR timings.
Otherwise I do use it for tilts, but rarely. I've gotten pretty good at feeling out the L-Stick on both the 1st Party GCN OG controller and the various 3rd Party 'modernized' Switch GCN controllers that Hori, PDP and PowerA (if you're wondering, by-far my favorite of these three and my overall go-to is the Hori. The PDP feels weird, the PowerA has janky shoulder buttons, hellacious snapback problems and loud buttons and the OG has snapback problems, missing buttons and weird QC issues with deadzones in my experience) make. Due to this, I'm able to consistently and effectively use tilts via the L-Stick, and I actually think I'm better at tilting WITH the L-Stick because of this. I DO use it for tilts on occasion, but only if I'm in very specific circumstances where using the L-Stick could screw me or etc. I also like tilting with the C-Stick with Piranha Plant in Ultimate because of his FTilt being a 2-hit combo, I've found that doing this combo with the L-Stick as usual will often result in me FTilting once, then immediately going into either a Smash or Dash attack after.
That's pretty much the jist of it, you can also buffer NAirs with the c-stick but the timing is strange and I wouldn't bother getting it down. The c-stick is best for spaced aerials, basically, though it's not ALWAYS best for aerials and nothing is going to hold up 100% in every possible situation. In terms of c-stick squelching and/or the macro inputs screwing with things.. you just kind of have to get a feel for it yourself and get used to it. Unless / Until Nintendo/Hal patches it out of the game, it's not going anywhere.. and I doubt it will because it's been with us since the beginning. If they haven't gotten rid of it by now, it seems they never will.
(This is the Sm4sh board btw, figured I'd mention that since you mentioned Ultimate)
