As someone who has an alt I've experienced several issues. First being the story quests are really terrible to have to do on two characters. At the launch of 2.0 finishing the main scenario on two characters was not a big deal. But now that there are two needlessly long addendums to the main scenario it really brings to light that the dev team is using fetch quests and stop gaps to try and extend what really equates to a very short actual story.

Second, grinding tomes sucks. My second character reached 50 just before 2.1 came out. I pretty much lost all desire to farm mythology tomes for both characters about a month later. Now I don't farm any tomes at all on one character and the other has only capped soldiery tomes twice since 2.2 came out.

Nothing wrong per SE with having alts, I'd just advise against trying to have two separate characters trying to progress in end game.