Is the use of the quotation marks necessary with expressions like "self-proclaimed", "self-styled", "so-called" and "would be"?

Solution 1:

They're sometimes called sneer quotes. They imply that the words/phrase between them aren't really that. When the author writes self-styled "artists" what she means is they're not really artists, they just call themselves that.

Solution 2:

When you say self-styled artist or so-called poet, you have already drawn attention to your belief that you do not agree that they are artists or poets.

The prose should speak for itself; the additional quotes are not necessary. (In my opinion, you don't need to draw even more attention by putting quotes around the noun.)

Solution 3:

The "scare quotes" imply the self-styling, so using both is redundant. As I like to bring up Strunk & White, remember that

Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subjects only in outline, but that every word tell.