A different design logic, and the logic of the blogosphere that preceded it, much more tightly prioritized following a blogger or poster and interpreting everything you see in light of who was posting it. The trust is placed in the account you follow.
"Persistent" reputation won't change that. Because on the internet nothing is persistent, without a central party enforcing it to be so. And as said above, the ones in charge of it now, don't want to enforce it really. You don't own your domain, you don't own your IP, you don't own your feeds, "content" etc. The infrastructure that routes people to your correct "reputation", isn't yours, it's controlled and owned by Big Tech, governments, and some smaller companies. Your feed can be taken offline or away from you in a whim. Access to your blog isn't yours. Not even if you host it on a rasberry-pi in your cupboard.
Aside from maybe some blockchain shenanigans, that is. Bitcoin and maybe Ethereum are the only decentralized "pseudonymous" identity providers that could step into this, but both are ridiculously costly and complex. And wholly unsuited to route content. Systems designed for this, like Tor, aren't really up to the task either. Just look at how insanely hard it is for "Content" that governments oppose, to remain online (e.g. on the tor network). Possible, but so complex, so fragile, that it's not a practical system to use en masse. Yet it's the only working system that comes closest to really owning content in the broad sense.
So it makes perfect sense to turn to the systems that have done this "persistent reputation", aka "identity" for centuries now: Governments. Compared to Big Tech, they're more decentralized - there are far more governments worldwide "doing identities" than there are FAANG corporations. Hell, even within the US or within my country alone, there are more. Compared with all other systems, we can control them, push them into a direction we want them to go - democracy. Far from perfect. Bad even. But the least worst way to have some "persistent identity" we can get. Unfortunately.
People remembering your handle is persistent, and people remembering if they had good or annoying interactions with you is persistent reputation that exists in the minds and interactions between different people. These are things people naturally do. If people don’t recognize your name and see it come in a trusted spot they just don’t trust you.
How tech breaks this is deprioritizes the people in the interactions. Instead of sending messages you use a “like” button to be intelligible to the platform. You don’t see the people putting stuff on your feed, it gets fed to a timeline that cuts it off from all context and atomizes it for your consumption. It’s the UI/UX that drives this. Even compare Reddit and HN with old forums. On forums like 25% of every post is just static bits of self-expression. There’s a PFP, the username is bigger, there’s often a big signature block. All of this makes the peoples’ posts feel like a person talking to you rather than text blocks that happen to have a tiny username and timestamp on it.
Edit: to clarify: You aren't your handle, because it can be taken away from you, can be injected, blocked, overridden, etc.
My technical rambling then went on about how or when we can make this "handle" decentralized so it cannot be taken away from you. Hard. As proven in practice. Almost impossible.
My name is maintained by a government. It is a "handle" that could be taken away too, but is governed in lots of rules, systems and regulations. My face (an extension of my DNA, I guess) is decentralized and owned by me: its the only handle that afaik no one can take from me.
So in social interactions, you're right: reputation, bound to "me", my face, my DNA is all that matters. But online we don't have this. The closest we can probably get is "my name", controlled by governments.
But I still believe that people will care about connecting with an actual person in meatspace. I just can't picture any other result except for complete and total burnout with the fakeness of the web.