Does this answer your question? "like I" or "like me"? The question is not identical, but the principles are the same. If one models on 'He is a teacher just as I am [a teacher], there's obviously a pull towards 'like I' here. But the 'accusative is default' pull is, as often, stronger. Use a pair of commas if you want pauses around the parenthetical, or keep it the way it is if you prefer smooth running text.
– Edwin AshworthApr 10 '21 at 10:36
Yes, pauses are definitely necessary to make the meaning clear. You could also say "Like me, he is a doctor/teacher".
– Kate BuntingApr 10 '21 at 10:39
@Kate I've found one example of zero punctuation in the first 40 hits in a Google search for << "he like me is a" -"does he" -"will he" >>, one of dashes, three of brackets, and the great majority, of commas. Zero punctuation is rare round parentheticals (as you say, it's often necessary to clarify or aid parsing). But for short, simple examples, it can be used to effect.
– Edwin AshworthApr 10 '21 at 10:49