I'll tell you: the community. Almost every one of the big problems that are discussed right now on these forums and other places are, in the end, directly related with how the community behaves in the game. Let's check it:

1) Speedruns. Yes, trash mobs don't give anything, and yes, the repair bill can be costly (I know it, I'm a tank). But really, and be honest here, do you really think that if this was any different we wouldn't have speedruns or that they would even be reduced in number? Some people always want to do things the faster and optimal way to get everything now. This is not the first MMO where speedruns exist (i.e. to use an example tossed by some people, speedruns in GW2, using every existing cheat to get everything faster, even when some trash mobs had the chance of dropping BiS gear or high level rare mats). Note that in the end the problem are not really the speedruns per se, but that people use the duty finder for them.

2) Fate farming. Let's be clear, at the end of the day everyone can do whatever they want in-game, but there are some things that are just weird and annoying for others. Just try doing a fate "as intended" without being part of one of those big zergs. Sometimes you can't even touch mobs to get credit. And no, joining a fate farming group shouldn't be required, at least not when you aren't interested in farming them or if you were in your way of doing something else, to start with. Fates weren't designed to be farmed, but to be something that you could find in the world while you were questing, traveling, etc. and that would make you feel that the world was a bit more alive. A lot of the time when I visit an outpust and I see all these people just waiting there on their chocobos/coeurls/unicorns/magitek armor, I can't help but die a little bit on the inside after imagining them (or finding them) rushing to the fates.

I could go on and on writing more failings (like the AFK one, that is also responsability of the community in the end), but these two are some of the most prominent ones (if not the most) that we have right now, I think.

Of course, SE is responsible of the game's design and can and should try to do something to fix any flaws. But, at the end of the day, it's the community the one who is being generally destructive with the tools that have been given to us to play, and most of the time it's on our hands to be responsible of letting everyone around us enjoy the game, improve this and not make it a miserable experience for everyone around us. It's not as if you had to sacrifice your first-born in order to make this possible (well, for some people it is), one just need to act with a bit of responsability and empaty over the rest of the playerbase. Yeah, I can keep dreaming, as that won't happen anytime soon, but that doesn't make it any less true.

Anyway, let's just hope that things get better after the free month ends...