No. The first amendment does not say "you have the right to free speech and freedom of the press/assembly, provided you use them responsibly/do not abuse them." A definition such as this clearly leads to the loss of the right.
That definition exists, is clear, and does indeed infringe the right. See Shenck vs. United States for the most obvious example.
You have to include case law associated with the Amendments, since that's how they're actually used. I of course don't dispute that the actual text of the Amendments is brief, but they aren't the whole definition of the rights.
Taken in total, they do in fact levy responsibilities on us to use those rights responsibly.
I can full well buy a gun and keep it under my bed for the rest of my life. In doing so, I am not using my right/responsibility for any personal or public good - in fact, other than ownership, I'm not using the right at all.
I cannot, however, shoot my mailman for no good reason. There are limits to the scope of the second amendment, as there are any other right. In this, there is the distinction between what is proscribed behavior for my right and limits to what I cannot do with my right.
I consider these limits to be a subset of the responsibilities. But the right isn't just about what you do as an individual. It's about what The People do, as well.
The other part of responsibility, however, is cultural and not codified in law -- except when it's relied upon for legal opinion, which does frequently happen. I don't think the US Constitution is the only way to govern nor do I think it would necessarily work in a different culture. But for our culture, as designed, the Framers crafted a set of laws that worked with our cultural identity. That identity includes a particular sense of duty and responsibility.
The First Amendment, for example. Societies can exist without this right (looking at you, Comrade Putin). But ours could not. People have the responsibility to use this right to speak out against governmental excess, just as they have the right to vote.
Sure, lots of people don't, just like lots of people don't vote. The system is suboptimal. But it works. As long as those rights are there, the option to act stays available, people can fulfill their duty when it counts, we're in good shape. More people would speak up and more would vote, I think, if we were ever faced with a truly severe problem. Let's say we had an election to determine whether California was expelled from the Union. Think the turnout for that would be ~ 40%? Or much, much higher?
If it ever got to a point where nobody voted or spoke up, to the point that The People no longer exercises its right, we'd have a crisis, even a revolution on our hands... Our government as it is would no longer function properly. Luckily I don't see this happening, ever.
Our responsibilities are collective, or so the Framers intended. Interestingly, the rights they enumerated were also collective. We've gotten selfish about the rights but we haven't stepped up as individuals to accept the responsibilities. Typical human behavior.
I'm not criticizing you, I've been just as guilty. Pretty much everyone has.
The only requirement I can see for voting (other than being of the appropriate age) is citizenship. Participation/contribution is incumbent upon being a citizen in a given society. So if you want to tie some sort of civil/military service to voting, you should require those things for citizenship.
No argument here.
I'm personally suspicious of tests for citizenship, since it's too easy for this to be subverted. We had slavery here once. It could happen again, but it must not. And it can't so long as we exercise our rights and discharge our responsibility.