Precedence and syntax in a language tells you a lot about what the language considers important. We take the 'quietest' syntax for things that we want to have fade into the background. Whitespace and periods are both very quiet syntax.
In math ' ' is often multiplication, in the lambda calculus it is function application.
We choose ' ' to have the tightest precedence in Haskell in a way that nicely emphasizes the importance of functions here. Admittedly we already have two awkward exceptions there that routinely throw folks for loops. @ syntax in patterns and the {}'s used by record syntax both bind tighter than whitespace application.
We choose . for function composition a.) because it on the keyboard and again, it emphasizes the importance of functions. Functions compose and you can make more interesting things out of the parts, the field accessor syntax you propose here does not compose particularly well.
With other solutions available today that this proposal actively makes worse, I can both read and write back to those fields
You're asking for (.), one of the most common symbols in Haskell code today to take on another meaning, furthering confusion for its current standard role, for it to effectively alternate binding looser than ' ' when you put spaces around it to tighter than ' ' when you don't while simultaneously changing semantics entirely.
Is it confusing to newcomers that (.) doesn't bind tighter than ' ' in haskell? Sure. But causing that to randomly change back and forth is more confusing still.
-Edward