From a game mechanics perspective, it makes total sense that you aren't seeing Legion invasions in every zone on Azeroth at all times right now. These areas are sort of "set in the past" and have to be for a player who is leveling up through them.
In the pre-expansion event, we saw several familiar zones getting hit with demonic invasions, and lorewise, we can assume that these attacks are continuing - in fact, they're probably having a harder time dealing with it given that the greatest heroes of Azeroth are all focusing on the Broken Isles situation.
Legion has really put the Horde/Alliance conflict on the back burner, which is actually a pretty big relief - the Legion's a big enough threat to deal with. But what I find interesting is how the two factions both lost their main leaders, and we're only getting glimpses of the resulting dynamics.
Let's start with the Horde.
We actually get a bunch of Sylvanas in Stormheim, but what is odd is that she doesn't even act like the leader of the Forsaken, much less the Horde entire. She has given herself a secret mission - so secret that she doesn't even tell us about it. So even after Greymane attacks her and her forces in the area, she compounds the fact that she left Orgrimmar (which probably needs someone handling the Horde's main strategy) but also abandons her own guard to strike a deal with Helya (we don't really know what the deal is - like what she agreed to in order to get that evil magic lantern thing.) She's the leader of this enormous coalition of powerful nations that really needs someone to lead them in war against the demonic onslaught (you know, like, a Warchief) but all we have seen her do is engage in her own schemes.
Basically, it's not looking like a good start for Warchief Sylvanas.
There are also a number of crises within the Horde leadership beyond her. Right now it seems like Saurfang is serving as the main representative for the Orcs. Thrall, much like his creator/voice actor Chris Metzen, is retired, and presumably is not interested in returning to any sort of leadership position. Indeed, Thrall seems to have lost some of his connection to the elements after using magic during a Mak'gora with Garrosh. My Tauren is fighting using the Doomhammer, so... do I get to claim that I'm a better shaman than Thrall? Cool!
The Darkspear Trolls have been on a freaking roller coaster. First they're accepted into the Horde, their leader is best buds with the Warchief. Then Garrosh comes to power and suddenly they're the pariahs. Then Vol'jin leads his rebellion and becomes Warchief, and the Darkspear find their fortunes reversed as they have a sudden position of great influence. Then Vol'jin dies.
Here's the thing: while there are people like Saurfang or Eitrigg who are in positions to lead the Orcs even after someone like Garrosh is deposed, can you name someone who can lead the Darkspear? As far as we know, the tribe is totally leaderless. Vol'jin inherited his position from his father, but Vol'jin wasn't a dad, so...
Basically, things must be chaos in Orgrimmar right now.
The Alliance is not quite as fractured, but it does have its issues.
Varian had earned a lot of respect from the other Alliance leaders, but Anduin has been a pretty popular figure as well, and he has provided continuity for the leadership of Stormwind.
Anduin is not exactly inexperienced, but he is certainly young. Still, at least he's staying in the capital and delegating. That said, it's not entirely clear that he has control over the Alliance (in fact, we don't know that he is technically High King yet.)
Greymane's actions in Stormheim clearly had support of the Alliance military (Admiral Rodgers was just as eager to strike against Sylvanas as Greymane) but one wonders if Anduin knew that Greymane was certain to attack Sylvanas when given the opportunity.
If Greymane's actions were contrary to Anduin's wishes, we haven't seen him suffer any consequences for it. While he gets away with it, I doubt that there will be much tension between the old wolf and the young lion, but if Anduin starts exercising his authority (again, an authority we're not entirely sure he has) there could be some big tensions inside the Alliance.
With Malfurion safe and having triumphed against the Nightmare, Tyrande is now leading the Alliance forces to assist the Nightfallen in liberating Suramar. The Horde sent (I believe - only on these quests on one character yet) Lor'themar Theron, who has shown himself to be pretty capable of working with the Alliance, and so far the tensions have been minor on that front.
The real Alliance leader to watch, though, is Velen. Velen underwent a horrific trauma pretty recently - being forced to watch his own son die at our hands during the invasion of the Exodar. (Given that his son became a demon, we don't know how permanent that death was, but either way it was a pretty bad day for Velen.)
We know that he's having the Exodar repaired with the intention of returning to Argus, and now that we know that we're going to Argus in 7.3, I imagine that Velen will be there with us (we might even take the Exodar to get there.)
Velen is the oldest leader of any of the playable races - in fact, there's some artifact lore about the Skull of the Man'ari that implies that he and Kil'jaeden were leading the Eredar for a very long time before Sargeras even showed up.
Velen has embodied the idea of having the patience of a saint - he basically acts with total benevolence, the way you'd hope a holy man would. His convictions do make him scary, though, like in Bloodmyst Isle (when's the last time you did those quests? Pro-tip: don't. Quest design has come a long, long way since Burning Crusade) when he commands you to basically kill every Blood Elf on the island.
But even when he has ordered some pretty extreme actions, he's always been calm and practical and wise.
Now? Now he's angry. And I think that we're going to see a very different Velen moving forward from here.