I will try my hand at another answer, is the answer
Gibberish
You can't read me, yet here we are.
You can't read gibberish, because, it doesn't mean anything, it's gibberish
As good as line 5, but just as far.
Line 5 doesn't exist, it means as much as gibberish does, which is not much
Doctors may share this trait.
Doctors are known to write in a confusing way, a borderline unreadable mess that's somehow understood by pharmacists
Or maybe just a half-eaten cake.
This maybe refers to talking with your mouth full, or the leftovers of the cake looking unappealing, and haphazardly placed
I think the answer is
Nothing
You can't read me, yet here we are.
You can't read "nothing", but you can read the word itself, and sometimes adding spaces (nothings) between words helps
As good as line 5, but just as far.
Line 5 doesn't exist, nothing to see there
Doctors may share this trait.
Doctors are allowed to share nothing about their patients, as per the Hippocratic Oath
Or maybe just a half-eaten cake.
There's no more of half of this cake, it's gone, nothing's left!