So I guess the right to a speedy trial only violated if the prosecution delay the trial for no good reason, but if the whole system is under resourced it doesn’t count?

That's true, but usually if it starts adding up, and not progressing fast enough, you'll start hearing the judge say hey, let's get on with all of this. That is of course unless we're having problems with not having an attorney etc. Although there are cases where that doesn't happen definitely. Or one side chooses to waive way, way too much time, for some ridiculous reason.