I predict that this will blow over, and won't be a big deal in a few years time once FOSS drivers for what is effectively just a new breed of TPM are released.
If in five years, it turns out I was wrong, I'll eat my hat. Although defining "my hat" by then might be difficult, as it'll probably be subscription based.
The specific functionality of remote attestation is so that a remote party can demand you prove what software you are running, and make it so that you cannot lie. Right now you're free to answer whatever you'd like, while running whatever actual software you choose, as long as you stick to the protocol. Protocols (especially well-defined open ones) are our traditional way of mediating between parties with mutually diverging interests. Remote attestation throws away such neutral mediation, making it so that the more powerful party can dictate what software the less powerful party is running.
One implication of a usable implementation of remote attestation is that a website could insist that you are running a certain OS, web browser, etc, and become unavailable to you otherwise. For example, banking websites have a clear path to doing this in the quest for their elusive "security". They already do similarly invasive things that alienate a small portion of users (eg complain about a device being "rooted", blocking VPN/datacenter IP ranges), and so it's a reasonable assumption that they'll adopt such technology for the same regressive goals.
And once it starts being a de facto requirement for users to have such functionality and it becomes easy for developers to use, it will trickle down to lower stakes websites - think anything that currently sees fit to harass you with a CAPTCHA. It's not simply Big Bad Microsoft that will push this onto us, but rather the entire market will gradually shift for "security" (ie corporate whims).
Will Free Software and the Open Internet still exist? Of course! Remote attestation does not prevent you from running whatever software you like on your local computer. But it will further bifurcate the Free user-representing world and proprietary WebTV land - imagine not being able to do online banking or shopping from your ergonomic desktop system, and having to do it from your phone that you also have to upgrade every two years. And the idea that some day ISPs will mandate this type of technology to connect to their network is far fetched, but still within the realm of possibility.
One caveat here is that if the remote attestation is only over the contents of the Pluton chip itself, then it cannot be used to dictate what software is running on the main system. I have no idea if this is the case here or not, but either way the integration of the chip onto the same die as the processor does not bode well for future development.
Furthermore, I do not believe the claim elsewhere in this thread that you could proxy such requests, as a secure remote attestation design involves the attestation result being used to generate a decryption key (eg a TLS session key) that does not leave the trusted software environment. So the system performing the attestation is unable to simply relay back what it has learned. There might be design shortcomings that or implementation bugs that allow for doing so, but the straightforward goal is to close those over time as for any vulnerability.