The more this signature is necessary the harder it becomes to deny issueing it to somebody.
I don't see how this changes much compared to nowadays. You can already require an ID for all kinds of these and the government already has total control over those. So what changes? China manages to ruin the lives of the people illegally born under the 1-child-policy for decades already, all without systems like eIDAS.
You can't protect yourself from authoritarian regimes with tech or good policy since those will just get ignored. Look at Trumps war with Iran, where did Congress agree to it?
I'm not a fan of these systems either, I also think software should be open and no vendor lock-in should exist. But I don't think this will change much to be honest.
Right now, physical ID is only required for government services, for the most part. But digital signatures can be extended later to gate all services and purchases, both online and physical, including non-government ones. For example, you can't host a website without a gov approved signature for each website.
Under a system like that, you would rarely find out when the gov refuses to issue a signature, or when any kind of injustice happens, really. Websites where people can talk about bad things happening to them will simply be denied a signature to legally operate, so they're given the ultimatum to "voluntarily" censor posts, or be shut down. It becomes impossible to have this very conversation on a public platform with any kind of meaningful reach. And they already have this kind of system in China, since you brought it up. In fact, they have domestic surveillance systems that make the Snowden disclosures look cute.
And in the EU it's already nearly the case. The dystopian horror that KYC/AML has become for honest citizens is beyond belief. And they're of course hiding behind the excuse that "bad guys are laundering money": but going after actual drug dealers, of course they're not doing that. We now have articles wondering if Belgium (where most of the EU institutions do live and where all these totalitarian laws are passed) has become a "narco-state" (where criminals make the rules).
People's life can be ruined when some employee, somewhere, decides he wants to bumps his SAR quota (Suspicious Activity Report): you can have a real-estate transaction fail (and have hence moreover to pay a 10% penalty to the other party) if either a notary, bank employee, real-estate agency employee decided that they've got the nostalgy of the Gestapo-time and decided to act like a good little nazi (yes, Godwin's law: for we're literally talking about totalitarism).
I recently had an notary's employee bother my brother for the source of funds when he bought an apartment... A quarter of a century ago. A quarter of a century ago and he was talking to my brother as if he was a criminal for he didn't have access anymore to the bank wire transfer from 25+ years ago. It's crazy for the exact same controls had already been done 25+ years ago when he bought the apartment. And the notary's employee fully knows that. (regarding that case my brother is currently looking into the national federation of notaries and he's going to file a complaint: he's got emails from that notary's employee that are totally out of line).
The problem is way too much power over the lives of others is put into the hands of petty people: petty bank employees, petty notary employees, petty public servants. The same kind of people who were all too happy to out jews during WWII and who were making sure trains would leave on time.
I previously had a folder where every single money transfer of more than 10 K EUR was saved: I know do it for every transfer below 5 K EUR. And these are to be kept forever for I know that me or my wife or my daughter shall invariably meet motherfuckers asking them "proof of the source of funds from 30 years ago when your father bought that collectible car" (worth less than 20 K back then btw, but worth 6 digits now).
Just fuck these systems and fuck anyone working on it and fuck all the nazis participating in it.