So, it's true that Archaeology is a bit broken.
1: Some archaeology finds are located inside of other assets (trees, rocks) or are positioned in places that is impossible to stand to collect (sheer cliffsides, in the air)
2: Some digsites just plain don't work. Surveying will not produce the spyglass to tell you where to go for your archaeology find.
3: Outside of Eastern Kingdoms and Kalimdor, it's impossible to visit digsites. WRONG!... Well, partially.
So here's the deal. The issue is very simple. When you learn archaeology of higher levels that would NORMALLY produce digsites in a new area, they don't have it scripted to do the first "digsite shuffle" in that area. So when your Archaeology reaches 300, there is no script(or it's busted), and it doesn't shuffle digsites in Outland(and Northrend, and Cataclysm, and Pandaria, and Draenor, and Broken Isles) to cause them to spawn. Cataclysm is lucky, because there are a few digsites on Eastern Kingdom and Kalimdor, so that once your at your 450+ Archaeology, completing digsites on those continents CAN make digsites spawn in places like Uldum and Twilight Highlands.
One would normally think "oh, then archaeology is broken and I can never get those", right? Well, that's not quite true. You see, there's a little magic that was introduced in Mists of Pandaria archaeology. That magic is called "Restored Artifacts". The common solves in Mists of Pandaria and up no longer sell for paltry(or if you're lucky, moderate) amounts of gold. Instead, the common solves can be crated into Restored Artifacts, and in turn traded in for other archaeology fragments. That's right, you heard it here, you can do archaeology in Pandaria and above, and use the common artifacts you get to purchase fragments for Outland and Northrend and others.
"But if digsites don't spawn when I reach the level or learn the archaeology profession, how can I go to digsites in Pandaria or above?" Right? You're thinking that, aren't you? The answer is... Magic. Not really, you just need a map!
These maps can be purchased from either the Lorewalkers' Quartermaster at the Seat of Knowledge, or the Archaeology Fragments Arakkoa in Warspear or Stormshield, all for the low-low price of 1 Restored Artifact. You do need to be Exalted with the Lorewalkers and the Arakkoa Outcasts to purchase these from the vendors (respectively). More on that later.
"But you said you get Restored Artifacts by completing common solves in Pandaria and above. If there's no digsites without a map, how do you get the Restored Artifact for your first map?"
That's easy! We have a good friend in Pandaria that will help us with that. For just the meager cost of one Spirit of Harmony, you can purchase it! Danky at the Shrine of Two Moons' Golden Terrace, or Krystel at the Shrine of Seven Stars' Summer Terrace each sell 1 Restored Artifact for 1 Spirit of Harmony. Motes are easy to farm.
If you want to be able to farm a little faster, stop by the Valley of the Four Winds and if you're lucky, you can say hello to the Yaungol by the name of Blackhoof. If you ask nicely (possibly using a sword, or fire, or some teeth), he may be kind enough to give you his Battle Horn, a reusable toy with a 2 minute cooldown that aggros all Pandaria mobs within 40 yards. He's normally having a nice walk in the field just north of the Stormstout Brewery.
So you've farmed your ten Motes of Harmony, and have your Spirit of Harmony (or maybe you just went to the auction house and purchased it, not judging). Just head over to your Spirit of Harmony Vendor and get your seed Restored Artifact! Once you have that, purchase your Lorewalker's Map and use it! It's as simple as that, and you'll now have 4 Pandaria digsites!
So far, I've found only 2 digsites in Pandaria that were broken to the point I couldn't do them (and one was only because I got unlucky and the first find spawned inside of a very large tree). But even if you get unlucky enough to get both of those, you'll have at least 2 others that are workable. You can likely get at least 3 completed common artifacts off of your first map, and you can always buy another map if you have too many broken digsites. The reason I suggest using your first Restored Artifact on a Lorewalker's Map is it's just so much easier to get the required rep. If you've already got Arakkoa Outcasts up, then by all means, go there with your first Restored Artifact.
Now reputation. (There are plenty of guides online, this is just a short overview)
This is probably the hardest part of either of them. Lorewalker's is by far the easiest in my opinion, because you simply need to fly around. I'm sure you've seen them while travelling. The large scroll that glows blue. When you click it, it brings up a short story and gives you progress on achievements. That's the one. You just need to find those. There are plenty of guides around that tell you where they are. Most of them are really easy. All you need is to read them. After completing an achievement, you get a mail from Lorewalker Cho, with a quest item attached. That item is how you get the rep. You use the item, go to Lorewalker Cho, and turn in the quest. Instant rep. After about 4, you'll hit Revered and can purchase the Grand Commendation, then it'll only take a couple more to finish off Exalted. If you don't get the Grand Commendation, you'll need almost all of the achievements/quest items, otherwise you only need 5-6 of them to get Exalted.
The Arakkoa Outcasts are a bit harder. You'll need to do a fair amount of actual quests for them in Spires of Arak. A bit more complicated than "fly around and right click these glowing things".
Now I will note, I have not done a lot of archaeology in Draenor, so I don't know how many/few of those digsites are broken. And remember, in a worst case scenario, if you forgot to save one of your Restored Artifacts for a new map and get stuck, you can always collect Motes of Harmony again in Pandaria to get your hands on another.
So now you have a steady income of Restored Artifacts. The rest is easy. Brann Bronzebeard at the Seat of Knowledge, the Arakkoan Archaeology Fragment vendor on Ashran, and Dariness the Learned in Dalaran(Broken Isles) will all give you a "Crate of Archaeology Fragments" of your choice, for 1 Restored Artifact. The Pandaria trader only has up to Cataclysm types. The Draenor traders have up to Pandaria, and the Legion trader has up to Draenor.
It's not the most efficient. It takes one whole common solve which is 40-60 fragments usually, to get one crate, and the crate will only have between 5 and 15 fragments in it usually. But it is possible!
Sadly, as of this moment, I do not have any way to get Legion fragments. But this will get you fragments for everything else, allowing you to actually get your hands on some fancy toys, BoA gear, Mounts, and Battle pets.
So it's as simple as that. You can still get all archaeology fragments up to and including Draenor, even without the digsites spawning normally. It just takes a little more effort. If you enjoy archaeology, or really want that one, specific solve... have at it!
If you don't believe me, I attached a picture showing both common and uncommon solves from Pandaria, completed just a few days prior to posting this.
Also, has anyone else noticed that Archaeology is just graverobbing... just after a really, really long time? Food for thought.