I find Twitter good. Many interesting people and ideas, that I'd never would've come upon on my own probably. I find the short message format forces people to really distill their idea. The SNR on my TL seems fairly high imho.
It looks like I'm using it exactly the opposite of your "real time event" mode. I follow people that are not journalists and don't comment on people nor events. Strictly ideas. There are other media much better suited to covering people and events and in real-time.
Not having an account - don't see how that can work. In incognito - which I presume is similar to me not having an account - I get to see only a single page with few messages, nothing more. And ofc not possible to follow accounts and thus shape the TL.
I never subscribe to trends, themes, areas of interest and similar devices used by Twitter to guess what tweets I'd like to see. Twitter is hopeless there (as is the rest of social media). Just "show me what the account I selected to follow posted" is plenty good. I can't divine why Twitter does not do that only, why the extra complications wrt what messages I see on my TL. It's not like it can't show me enough adverts while showing only messages from accounts I follow.
Aside: I'm mystified how one goes from "don't like it" to "should not exist". Why, what's wrong with "live and let live"?