The proposal explicitly goes against “more fingerprinting”, which is maybe the one area where they are honest. So I do think that it’s not about more data collection, at least not directly. The token is generated locally on the user’s machine and it’s supposedly the only thing that need to be shared. So the website’s vendor do get potentially some infos (in effect: that you pass the test used to verify your client), but I don’t think that it’s the major point.
What you’re describing is the status quo today. Websites try to run invasive scripts to get as much info about you as they can, and if you try to derail that, they deem that you aren’t human, and they throw you a captcha.
Right now though, you can absolutely configure your browser to lie at every step about who you are.
I think that the proposal has much less to do with direct data collection (there’s better way to do that) than it has to do with control over the content-delivery chain.
If google gets its way, it would effectively switch control over how you access the web from you to them. This enables all the stuff that people have been talking about in the comment: the end of edge case browser and operating systems, the prevention of add blocking (and with it indeed, the extension of data collection), the consolidation of chrome’s dominant position, etc.

Yeah, moreover you give server admins the illusion that they CAN control what happens client side, which is bonkers.
Honestly the most infuriating thing in this whole controversy is that the proposed approach fix almost none of the issues that the authors say their proposal should fix.
What it does however is break the open web principles in major ways.

As other have pointed out, it goes way beyond ad-blocking. It’s a complete reversal of the trust model, and is basically DRM for your OS:
Right now, websites assume rightfully that clients can’t be trusted. Any security measure happens on the server side, with the rationale that the user has control over the client and you as a dev control the server. If your security is worth two cents, you secure server side. This change propose to extend vendor power, by defining a set of rule about what they deem acceptable as a client app, and enforcing it through a token system. It gives way too much power to the vendor, who gets to dictate what you can do on your machine.
We actually have a live experience of how that could go down with safetynet on android. Instead of doubling down on the biggest security issue there (OEM that refuses to support their software for more than 1 or 2 year after release which, quite frankly, should be universally considered as unacceptable), google decided that OEMs should be allowed way more trust than the user. Therefore modifying your own OS in any way, even if it’s ripe with security flaws to begin with and you’re just trying to fix that, breaks safetynet. If you break safetynet, “critical apps” like banking apps stop working altogether.
The worst part is that there are ways to circonvent safetynet breakage, because in the end, if DRM taught us anything, it is that if you control the client and know your way around, with enough work you can do pretty much anything you want with it. So bad actors are certainly not kept at bay, you just unjustly annoy people with legitmate usecases or even just experimenting with their hardware because in the end, you consider that your user are at best dumb security flaws, at worst huge cash machine, often both at the same time.