> The entire legal system is designed to punish people from the moment of arrest through conviction.This is indeed true, and a problem, and if you have ideas for how it can be improved, I'd be all ears.
But, I've not found any country/region/system that doesn't have some level of this problem. The US's system, of required public formalities for certain charges to proceed, & certain guarantees of time limits, & avenues for release/acquittal, is pretty strong compared to anywhere else. (In the Netherlands, a software developer has been in custody for a couple months now without any specific charges/case being revealed to him or the public.)
And, it's kind of inherent to any system for there to be some margins-of-abusive-discretion that are hard to eliminate, and time-limited steps-in-a-judicial-process where unavoidable "punishment" comes even from a process that hasn't decided yet. So mentioning the mere existence of such unevenness doesn't really say anything, either way, about the relative value the US culture, or legal system, puts on free speech.
What does shed light on the value the US puts on free speech is whether such irreducible annoyances are larger or smaller, with respect to speech, than other countries and other eras. And at every step of US history, even dark days like say Wilson's persecution of WW1 draft-resisters, or Hoover's mid-20thC persecution of civil rights movements, the US had more space for speech, more defenses for those accused of speech-related offenses, and larger cultural/social support (in both legal/political action and the commercial 'blocking-and-tackling' of actually publishing & disseminating speech without outsider veto) than almost anywhere else.
That's where people should be able to see the real, high, & enduring value the US has always put on free speech, if not neurotically obsessed on only negative examples, & scattered hypocrisies, blinding them to relative-magnitudes.
If Americans have not consistently enjoyed equal free speech – but even in such inequality, almost all Americans had far more free speech than they'd have had anywhere else – then that's more a knock on the US' value of equality, while confirming its leading value of free speech.