You would love one of my favourite books, City of My Dreams by Per Anders Fogelström (and the rest of the books in the series). Not only does he not use "he said she said" annotation but also completely forgoes quotation marks of any kind and relies only on the author's ability to change the tone into a more dialoguical one and dialectial spelling to get the point that someone is speaking across.
It's one of the stylistic choices I admire the most, to be honest, and wish I was able to implement without sounding pretentious.
Well, to be fair, if this Fogelström guy also excluded quotation marks it sounds like he's going the whole mile, and if it's even readable it sounds like a mark of a talented author. ELaIC has a tendency to thrust you into the Infinite Featureless Demiplane of Dialogue whenever the main character initates a conversation (although as I progressed through the work it became apparent that the actual way you are supposed to differentiate dialogue here is the fact that the kid basically exclusively communicates by asking questions using unnecessarily large words.) It sorta reminds me of those parts of the later Harry Potter books where, like, Snape and Dumbledore or whoever start talking and it's just "'thing' he said 'other thing' he said 'counterthing' he said (ad nauseum)" and it drags on so long without any proper nouns that if you lose track of who's talking you have to backtrack to the last thing that obviously came out of one character's mouth and count lines.
But seriously, this thing reads like the kid's hopped up on a double dosage of amphetamines. He starts the book by going off on a tangent about limousine rides and repeatedly goes off on similar turns of strangeness and nonsense that seemingly only serve to accentuate how "adorably precocious" the main character is. Most of the non-dialogue just comes across as a stream of consciousness; for instance, the main character randomly interrupts his description of how he's traveling to Queens for the first time to talk about where, exactly, the Bronx ends and Queens begins. A side character has the full description of "looks like [the main character's] mom, has huge boobs", which is problematic because literally the only description of the main character's mom we get is that she looks pretty. We don't find out that the woman is in her forties (but apparently looks uncannily young) until halfway through the chapter.
And dear god, I can't stress how much the protagonist bugs me. He reminds me way too much of myself when I was his age--obsessed with repeating random, questionably useful trivia at people, going off on weird tangents all the time that have very little to do with anything else, touting literature he barely comprehends as his favorite book, and generally trying to grow up way too fast. He always talks about "inventing" things, by which he means stormbraining weird hypothetical ideas and acting proud about it. He uses excessively large words all the time, but he always uses the same ones. And all the adults in the book love him for all of this. This is probably more of a personal qualm than anything, honestly, but this kid feels like a cheap facsimile of a person I was aeons ago and I hate it.
This is more of a nitpick, but the main character loves Shakespeare, and his participation in a production of Hamlet is brought up as a side detail multiple times, but the author has clearly never read Hamlet, because the main character is apparently playing Yorick. How he accomplishes this task without being decapitated is beyond me.
Note that I am 1/3 of the way through the book and am merely offering (rather irritated) first impressions. If this reaction was intentional then I will be amazed, but I have a sinking feeling it wasn't.