I know, right? "I've said something in a public space but think I can prevent others from quoting me". Um. Not how the world or our free society works.
There are lots of "practical" pieces to this, as others have mentioned.
Just to be clear, though: The signatures you've noticed, if properly phrased, do carry the force of law. The only requirement for an author to copyright written material is to create it in fixed form (paper or computer or...). No other form of registration is required by US law to establish copyright; it exists from the moment the work is "fixed in tangible form", including machine readable. For more details
click here (US Government copyright site).
Furthermore, TMC is not "Public Space". It is privately owned, and chooses to make content available via certain distribution channels. The copyright notice at the very bottom of the main page also carries the force of law.
Again, I recognize there is a practical side to this, and we can debate "Fair Use", which is a very complex topic, mostly codified in court precedent and not legal code. We could also debate other aspects of copyright law... but there are some parts of copyright law that are just facts. Despite the commonly held mis-belief that "free society" or "public space" somehow affects copyright. It simply doesn't.
If you want a crystal clear example: A poet still owns the copyright on a poem, even if they choose to exhibit that poem on a wall on a public street. Total control regarding further reproduction. By law. Again, there is a practical side... people may copy the poem, memorize it, recite it, photograph it, and more, in practice. Nonetheless, legally, the copyright remains with the poet. Period.