As opposed to the 3rd closer to their natural like in sc2? It forces you to use nydus to reinforce and saturate and it seems illogical
The reality is that the third base in most maps has been balanced to be mineral only, or far away enough so Zerg cannot get 3 bases with gas so easily, otherwise 3 gas Zerg before mid game is way to strong for even Protoss to survive mid game, not even to say Terran that already REALLY struggles with early game Zerg. That answer 50% of your question, also in 4 corner maps Zerg prefers to take the base that is far because it is most of the times also the natural of another main, so Zerg asy ou probably know already, and as a general rule ,during mid and late game always needs to have one base more than Protoss and terran, so taking that “far” natural makes it easier latter to take the other fourth corner main protected by the third base.
There is another reason which is more obscure and that is that most Terran attacks rely on position and timing, having Zerg bases in different spots forces Terran to have even a harder time deciding where, how, and when to attack, moving marines from one point to the other takes a few minutes and meanwhile Zerg can adjust defenses accordingly punishing Terran timings. If the third is too close Terran can change the Barracks rally point and keep Zerg locked in a small sector of the map, while having a third in a far places gives time to Zerg to move units around etc.
It’s easier to come down the ramp to take a 4th
In ZVT taking a 3rd for Zerg is really hard, but really important.
On many maps you have hard time defending your third because the third has multiple entrances, and zerg doesnt have enough minerals to build sunkens at both your natural(2nd base) and third base.
Often you take your third base when you have critical mass with Mutaslisk or lurker. Since there you will have a power spike vs Terran and with lurkers you can hold the ramp of your third on a other main, while getting most minerals and and easy 4th base.
If you take it before you are gambling and Terran will mostlikely kill it.
Of course it also depends what the opponent does.
Maps like Eclipse has @one@ ramp at the 3rd base, which allows to take early 3rd base, but this also stretches your defences and minerals quite. A thing the Terran can abuse.
An other reason is the fact that Zerg cant attack head on the terran army, most times and Terran will make the zerg pay to much, even if the zerg would win the battle. Zerg needs to manvour and pick up stray units and win in detaill.
A third on the other end of the map makes the Terran split its forces and lets you send units from either production facilit into the map to threaten surrounds, attack reinforcing units or threaten backstabs into the terran heart/ base.
This problem we see on Eclipse aswell, when the Zerg takes the near 3rd base. Terran has the ability to park his army infront of the nat/ 2base of zerg, while also quite of shutting down the path of the 3rd.
An other aspect is the fact that distance can help the zerg, since as you mentioned the Nydus lets the Zerg be on both bases. While Terran can only be at one location or split his army. An other aspect is that each hatch is a production facility, so the saturation isnt that big of deal. And most good zerg players will know if, and when to send some drones from the main base.
to take 2 base as 1, only protecting 1 entrance