I notice that NPCs in Eberron are very low level.
Most characters in most settings are very low-level. Even Forgotten Realms.
Can anyone tell me why this is?
A bit of a can of worms. When Eberron details first came out, the fans started talking about it like it was the anti-Forgotten Realms. I don't believe WotC ever said this, but I suspect it was part of their marketing strategy.
In Eberron, the GM has to avoid putting a pit fiend (a high-CR creature with damage reduction, specific regeneration and teleport without error
at will) into the setting for fear of massive destruction - at least not just at any time. Said monster would be a major villain, a counterweight for the She-Pope or something along those lines, and the GM has to think about this beforehand. (Also, a pit fiend is not a suitable challenge for a party of, say, 12th-level heroes.)
Contrast to FR, where the high-level good-aligned NPCs are so powerful that the GM needs to invent excuses for why they're
not dealing with whatever villainous doings are afoot. The novels only make this worse - Khelben, for instance, has a spy network so extensive he can tell when a single drow is entering Waterdeep. (His Gather Information score isn't that good either!) Of course, at least some novels buck the trend... apparently Drizzt avoids any area (except where Alusair is) that has epic-level wizards. You can drop a pit fiend into the setting and the common adventurer won't even notice; they're too busy dealing with the latest Zhent plot. (Oh wait, it was a false flag operation, actually a Red Wizard plot, but they're being manipulated by the Cult of the Dragon... You get the point.)
For those who have played Eberron campaigns how do you deal with it?
Use appropriately-leveled NPCs. The Lord of Blades is 12th-level and a terror. There just aren't many good-aligned NPCs to challenge him, and they're probably crawling through some hellhole in Xendrik anyway, or dealing with a plot in a far safer place than the Mournland.
What is going to prevent high level individuals from overthrowing the weak NPCs who quite often hold important positions?
Even in FR, the king of a kingdom isn't necessarily a 10th-level fighter/3rd-level wizard. They might be a low-level aristocrat. They're probably being manipulated
anyway.
But in Eberron it's going to be really hard for famous Evil Lord #337, ex-Pal10/Blackguard 10 to openly rule any place. (Even King Kaius III, who is really Kaius I, has to pretend he's his own grandson in order to rule his kingdom.)