We've covered in the past how the best way to gear for PvP is to grind justice points, and I have recently experienced this - since I wanted to get some pieces of Season 14 for transmog (and to do some PvP on the side, since I like running random BG's) I spent the past couple of days capping honor so that I could pick up several pieces as soon as possible. This led to running dungeons for justice points. Lots of dungeons. And this led me to realize that justice points themselves have a lot of uses - picking up older gear to catch up, converting to honor for PvP gear - but they feel strange and antiquated.
There's literally two ways to get them in the current endgame - run scenarios or dungeons - and they only upgrade blue dungeon gear, so their use as an upgrade currency is fairly limited. While you can in fact also buy them with honor, that would have been self defeating in my case.
In fact, since they have a much larger cap than valor points (4000 to valor's 3000) and they don't have a weekly limit on how many you can acquire (whereas valor has a rigid 1000 point limit in a week) you could argue that justice points are in fact more valuable to a player who isn't already raiding than valor points are, which is why the fact that it's easier to earn valor (weekly quests, daily quests, dungeons, scenarios, heroic scenarios, raid finder, raiding) than justice is kind of baffling. Right now, you can't buy any new gear with valor - none was introduced with patch 5.4, and unlike justice points you can't convert valor to purchase PvP currency, so you can't even convert it to PvP gear. Valor is only really useful for upgrading epic gear - the only valor gear currently available is on the Shado-Pan Assault quartermasters, introduced back in patch 5.2.
This is not to say that either currency is hard to acquire. It's more that justice points are tedious to acquire - there's no other way to get them besides dungeons, scenarios, or buying them via honor (honor and justice convert to each other at a 2 for 1 ratio - you spend 500 honor for 250 justice, and vice versa).
I find that in practice, justice points have become cumbersome, while valor points have become quixotic - either you use them to upgrade, maybe buy a couple of pieces of gear that you then replace in a raid finder group, or you don't use them at all. If you need gear that you can buy with valor points, you probably get more out of farming for Burdens of Eternity - they reward higher ilevel gear, ater all, and it doesn't feel like you wasted points to get it. It's a strange sensation to feel like a currency has no real purpose, and yet is too valuable to spend on the off chance you'll get an upgrade and want to, well, upgrade it more.
Justice points, meanwhile, you'll spend like water. To be honest, most of the time I only notice my justice points when I cap them and suddenly can't get ride of the boxes in my inventory from running scenarios. That's because, while they have a host of uses if you're below a certain gear threshold, that threshold is easily reached via the Timeless Isle, making spending justice any further somewhat purposeless. But they accumulate fast (100 per heroic dungeon boss, 60 per scenario) so you'll end up spending them, if on stuff you don't need or want, just to clear that cap.
I think it's clearly time to simplify these currencies in some way. Justice points even having a cap at this point makes no real sense - they don't provide so much of a benefit that anyone is willingly hoarding them. If it's a concern for PvP conversions, we can simply dump justice on big PvP season patches or put in a cap on how many JP you can convert to honor in a week (but frankly, is letting people hoard JP and buy an entire set of last season's PvP gear really that big a deal?). An easier solution would simply be to ditch justice and honor (or valor and conquest) and have one currency for PvE, and one for PvP. You could treat it exactly as valor and conquest do now, but have small amounts of valor from dungeon bosses, and have previous season gear sell for much small valor costs. The same with conquest points - since rating already acts as a gateway for PvP players, letting them get conquest points for non rated BG's and buy last season's PvP gear for conquest at a large discount shouldn't really be an issue.
In the end, keeping track of four currencies is kind of absurd. We're simplifying statistics and getting rid of reforging, why not make currency equally easy to track?