As far as asserting more than $20 in damages and getting thrown out of court on jurisdiction: tons and tons and tons. Happens all the time. Here's an example: https://scholar.google.com/scholar_case?case=768942503267893.... This was back when the jurisdictional requirement for diversity cases was $50,000 (it's now $75,000). Plaintiff didn't allege enough damages, and he got thrown out of court.

You may want to reconsider your assertion that it works this way because you haven't made this argument in court. Lots and lots of people have tried to argue that clicking can't form a binding contract, and they lose. Have a look at https://scholar.google.com/scholar?hl=en&q=clickwrap&btnG=&a... for gobs of cases where clickwrap contracts have been held valid and enforceable.

Here's what will happen after you file your lawsuit against the company with an arbitration clause. First, the company you're suing will file a motion to compel arbitration. You'll say "wait a minute, I didn't agree to shit." If you're lucky, the judge lets you do some limited discovery on the issue of whether you agreed. You'll get to take some discovery, but so will they. And what they'll do is take your deposition. That means that you have to show up for them to ask you questions under oath. This isn't in court in front of a jury, but you can't lie, and everything you say is recorded by the stenographer. Here's how that will go:

Q: Mr. Jsprogrammer, have you ever created an account on ZZ website?
A: Yes.
Q: And what is the username of that account?
A: jsprogrammer.
Q: When you created that account, did you use ZZ website?
A: Yes.
Q: I'm handing you now what's been marked for identification as exhibit 1. Do you recognize this?
A: Yes.
Q: What is it?
A: It's the registration screen for ZZ website.
Q: And is this how the screen appeared when you created your account?
A: I don't know. Probably.
Q: Would it be fair to say that it is at least very similar to the page that you saw?
A: Yes, that would be fair to say.
Q: On the document I handed you, do you see the checkbox next to the words "I agree to the terms of service."?
A: Yes.
Q: When you created your account, did you select that checkbox on the screen?

Now what do you do? You can say you don't remember. Or you can say yes, because you know you checked it. Or you can say no and commit perjury (not a good idea).

Deposition in hand, they'll amend their motion to compel arbitration. They'll include a sworn declaration from their developer lead, saying that there is literally no way to create an account without agreeing to the terms. They'll attach the terms, with a sworn declaration from the guy who's in charge of updating the terms saying that these were the terms, as they appeared, on the day you created your account. Finally, they'll attach your deposition, where you (if you didn't commit perjury) don't deny that you agreed to the terms.

So now what's the judge going to do? When the company refuses to turn over their source code and you ask the judge to make them turn it over, she is going to ask you why you didn't deny checking the box. You're not really going to have a good answer for that. Then, she's going to come to the natural conclusion: it's because you did check the box. Then the judge will dismiss the case, and you'll go to the arbitrator.