Two peeves in one here:
The "/s" is just punctuation, same as "!" or "?" or even ".", which was a radical suggestion at one point. Punctuation isn't bad, it's not necessarily good either, but it is often useful. It should be judged based on whether it improves the ability to communicate via the written word by encoding nuance that would have been expressed verbally.
And A Modest Proposal isn't comedy, it's also not sarcasm, it's satire. Modern satirists may have confused themselves into thinking that the point of satire is to be subtle, but this is a disastrous idea. Satire is political commentary, it's supposed to be so over-the-top and starkly obvious in its intent that it cannot possibly be misconstrued as accidentally arguing in favor of what it's trying to argue against. This is why, for example, Paul Verhoeven's Starship Troopers is bad satire: if someone has to ask "is this satire?", or someone has to helpfully point out that something is intended to be satire, then it's bad satire by definition.
/s is not punctuation, it's an explanation. And explaining the joke kills it, and also insults the audience. Sometimes the ambiguity of a statement is itself powerful, as it reveals how one side can wholeheartedly believe something the other finds absurd.
One should only use /s if the comment is really so devoid of absurdity that it can be misinterpreted.
GOOD: Trump has done a lot of good for Americans /s
BAD: Trump is the greatest human ever born and is entitled to prima nocta with all brides /s
Re: sarcasm vs satire. You're mostly arguing the dictionary. The /s "sarcasm" markup is used when satirizing some POV, not just strictly for sarcasm.