If end of line always means end of statement, by all means get rid of semi colons. If some non-trivial algorithms is used to infer end-of-statement boundaries that is more complicated than detecting end-of-line, then...there will be subtle problems.
I went through this transition before in Scala, the error messages got a lot worse after semi-colon inference was added. I wound up telling people to add semi-colons to their code when they were scratching their head at some sort of parse/type error message.
Semicolons are distracting, both reading and writing, and mostly useless. If it's not "noise" in a technical sense, is it not still a bad thing? I don't think this should be a complicated question.
Two choices dictate a terminator: (a) free form 1D language like C vs 2D language like Python or Haskell, and, (b) support for assignment statements x = y and the like as in C vs all statements starting with a keyword as in say ATS. I personally do not like the semi-colons either.
And simpler to parse has another benefit Given an effort X spent writing the parser, users of the language get better error messages
Also, I do not think of those semicolons as noise They make text easier to parse for humans, too That's why you see most people end sentences, paragraphs and HN posts with a 'superfluous' period
EDIT: Some people will find the above quite readable I am somewhat in that camp Problem is, however, that in English and other languages capitals like I and E are not guaranteed to be sentence starters That muddles the waters considerably Many programming languages have worse problems.