Sentence fragments are ubiquitous in spoken English, where tone of voice, gestures, and body language help convey meaning and where the opportunity to ask questions prevents much mis-communication.
And sentence fragments are frequent in written English, particularly informal English. But an English reader expects a subject and a verb. When both are missing, it requires an extra effort by the reader to parse the fragment. So I view it as a discourtesy to me the reader if the writer is too lazy to write "It's."
Now if you are reporting speech, then of course you will write in sentence fragments to be realistic. But otherwise it seems that omitting "It's" subtracts rather than adds to the clarity of your prose.