Why zerg taking a third to P's FFE or T's double Command Center is only an equilibrium?

It mostly comes down to larva and the inefficiency of Zerg units in larger numbers as well as the gas requirement for more efficient lategame units.

1. Zerg need larva to produce, larva comes from hatcheries, 3 hatcheries with good injects are about equal to 2 base terran or protoss production and if you are building hatcheries anyways, you might as well place it at a new base.
   With sufficient creep spread (which is extremely vital) and good scouting the opponent won't be able to kill it off early game anyways.
   If there is the chance that he might kill it, for example when you scout some sort of all-in, it's ok to get the third hatchery in your main or natural (aka macro hatch) and delay the third base but usually you are safe enough to just take that base.

2. In midgame the cost efficiency of Zerglings and Roaches falls off rapidly, which means you either need a lot more of them or you need a lot of gas for higher tech units (point 3 below). A lot of units means a lot of larva and resources which means you need an extra base.

3. For your mid- to lategame units (mutalisks, infestors and broodlords) as well as the very critical upgrades you need tons of gas, which means you have to get your 6 extractors relatively early to build up the gas so you can get out a critical number of units once your tech structure/research finishes.

As for having to pressure with mutalisks you might want to watch Stephano who has a playstyle that completely skips those and goes from infestors straight to broodlords. Considering that on the TeamLiquid TLPD he's currently rank 1 worldwide it doesn't seem to be a bad style either. Many people who play the mutalisk style get stuck there since they use all the gas for mutalisks and then don't have any gas for higher tech units like broodlords that you really, really need in lategame, especially against protoss.

The basic reason for needing an additional base is that if your army matches the size of the other players army. 9/10 times you will lose a head on fight simply because Zerg is not meant to stand head-on to fight battles.

More bases the the opponent means a higher income. It means you can produce the amount of troops needed and fast enough to kill the opponents army and replenish your own faster. As for more points to defend. As zerg take smart expansions think where they might attack and place your expansions in logical places. If they attack a dead-end for example. Box them in and surround their army or counter attack while the entire protoss army is away. Don't be scared to expand as zerg as its main advantage is typically map control. Scout where he is going and stop those incoming attacks. More bases can also allow you to tech up earlier etc.

Harass anyway you can. Muta harass can be easily shut down by a few cannons or a few turrets but can still prevent expansions and put a good amount of pressure on.

But overall, a zerg won't be able to produce fast enough on two bases against an opponent on the same number. It is zergs advantage to expand faster then the rest.