I'm not saying it doesn't logically follow, I'm saying it shouldn't legally follow. Exercising your legal rights should never have negative legal consequences.
Consider pleading the fifth. You can't be compelled to incriminate yourself. That doesn't just mean they can't coerce a confession out of you. It also means that the law does not infer guilt from a refusal to testify, even though logically a person who refuses to testify is more likely to be guilty than one who testifies freely in their own defense. If you couldn't be compelled to testify, but at the same time your refusal could be considered evidence of guilt, then you don't really have the right not to testify.
Same sort of thing here. If exercising your right to a trial increases your penalty then in what sense do you actually have that right? To put it in starker terms, imagine if people who previously spoke critically of the President were given a harsher penalty than those who spoke positively. That's a clear free speech violation. If exercising your free speech rights can't increase your penalty, exercising your right to a trial shouldn't either.
I understand the constitutional point you're making, but I think we're conflating two things: exercising your right to trial, and showing remorse for what you did.
The right to trial isn't being penalised. You get a fair trial either way. What's being rewarded is accepting responsibility and saving the court's time. That's not the same as punishing you for exercising a right.
I'll grant that when the sentencing gap is extreme, the distinction becomes academic. If you're facing 20 years at trial versus 2 for pleading, then functionally you're being coerced regardless of the theoretical justification.
But in principle, rewarding people who show remorse is part of justice. Someone who accepts what they did and shows contrition is different from someone who forces the state to prove its case. Both have the right to trial, but treating them differently at sentencing isn't inherently unjust.
The question is whether the gap has become so large that it's effectively coercive. That's an empirical question about how plea bargains operate in practice, not a constitutional one about whether they can exist at all, which, if I understood it right, is your position.