Why are all quasars so far away?
If the universe is homogeneous, we should expect to have a homogeneous distribution of quasars, but all of then seem to be far away from Earth. Why is that?
There are essentially two reasons.
First, quasars are rare objects, so even though they are homogenously distributed on large scales, the average distance is large. Moreover, the brightest quasars are even rarer, but visible to large distances, so their average distance is even larger.
Second, most quasars were most active at redshift $z\sim2$. This is thought to be because quasar activity is triggered by galaxy mergers, which bring gas into galactic centres so that the supermassive black holes can be fed. Galaxy mergers and star formation peaked at $z\sim2$.
Finally, there is some bias in the sense that astronomers are looking for the most distant (and hence oldest) of objects, because they are more interesting than nearby objects when it comes to learn about the formation history of the universe.
You have stumbled across a profound observation and almost grasped one of its most important consequences.
There are two forms of the so-called cosmological principle. There is the more limited cosmological principle, which to paraphrase, says that the universe will look the same in all directions to any observer anywhere in the universe at the same time (i.e. at the same cosmological epoch). There is also a Perfect Cosmological Principle, that says the universe is homogeneous and isotropic in both space and time.
The Perfect Cosmological Principle was the underpinning for the steady state theory of the universe. However, one of the most obvious objections to this was that we can see that the universe has evolved in time. One of the first realisations of this was indeed the observation that quasars were more common at large distances and hence more common in the past.
Thus this observation tells us that the characteristics of the universe are changing with time and therefore that the Perfect cosmological principle is incorrect.
The more limited Cosmological Principle meanwhile remains. It ony asserts that everything should look the same to all observers at a given cosmological epoch; it does not require the universe to look the same at all times and therefore does not require the density of particular types of astronomical objects to be constant with distance.
Quasar activity peaked at moderate redshifts due to the required feeding processes of active galactic nuclei and the competition between the merger activity of gas-rich galaxies and the quenching caused by massive star formation and negative feedback from the AGN themselves. It appears that the "sweet spot" for comparatively short-lived phases of "quasar activity" is at redshifts of 2-3 where there was significant merger activity and the transport of gas into the central regions of galaxies, but that there had been insufficient time to fully exhaust the gas in galaxies with central black holes.
The discussion of the Cosmological Principle above is very relevant, but it is possible that so is a (weak) application of the anthropic principle - in other words if we were in a region of extremely energetic physical phenomena, such as quasars, we would be unlikely to exist - as the evidence suggests that the development of intelligent life takes a considerable time and highly energetic events are likely to disrupt that.
in the early universe there was more diffuse matter in gaseous form available to the black holes. The galaxies were more foggy with diffuse matter and less void, so a BH travelling through a galaxy could catch a continuous cloud of matter as it went along, resulting in huge capture rates. Back then, most gas had not yet collapsed to form stars, there was more fuel available for both the feeding of black holes and the forming of new stars. Much of that fuel was subsequently consumed in the formation of stars during the first few billion years after the big bang.
"Far away" = "very old" in cosmology.
All quasars are far away because all of them are old. These are objects that occurred when our bubble of Universe was young. So when our telescopes look far into space, they look back in time, and see a lot of quasars then.
They're mostly giant black holes devouring gas and dust and cosmic junk, of which there was lots back then near these black holes. After they vacuum clean their environment, they calm down and the quasars basically turn off.
There are essentially no quasars forming in our time. Therefore there are no quasars visible nearby.