I'm against them - for several reasons
The first is that it is hard to know what exactly will trigger a memory for people. It seems very.. I can't think of the exact word, but you have to be very arrogant or condescending or something to look at a piece of art and say "Somebody could be traumatised by this! I must make sure they don't see it!". It seems like getting offended on behalf of other people for the purpose of showing how morally superior they are, creating a controversy where there probably wasn't one.
The second is that the term get thrown around so much that it loses it's impact. I think if it was left for the really high-impact stuff, it might be OK. But people will always argue that their particular trigger is important and should be considered just as valid as other people's. When it gets to the level that was in the article, people protesting about a sculpture of a man in underwear, it becomes a joke. Do these same people also protest the big billboards of Dan Carter in his Jockeys?
The third is more of a philosophical reason. Are we really helping people by sheltering them from potentially upsetting situations? Again, I recognise the argument when it is a very high-impact sort of thing. But i think exposure to related situations over time is more beneficial and toughening - it's not like trigger warning are going to be everywhere, so you will still encounter them. A bit of common sense can let you know what not to look at in many cases.