Gathering global timers have to go... Personal Cooldowns for nodes.

[Eidolon]

2 people = 12 nodes per person per time.
3 people = 8 nodes per person per time.
4 people = 6 nodes per person per time.

Ect ect.

Sorry you don't understand this. The nodes may have the same timer but they are contested. Meaning there is only so much generating at a time. Making them uncontested would greatly lower the value of said items.

Hacking is part of the game unfortunately, and everything should go into equation when your doing math.

The second you make zones uncontested is the day you see 100 bots teleporting around all farming 1 node every hour. It will make it WORTHLESS.

I'm extremely confused by your post. It sounds like you're aying only a certain number of people can hit a node because it reaches some capacity?

But.... That's not how they work at all. Everyone online can hit that node (Secondary Edit-in: AND THEY WILL GET THE FULL BENEFIT OF THEIR NODE as determined by their gathering/perception) if they're in the area - weather it be 5 or 500 people, the only limit is you can gather from an unspoiled node only once as your individual character.

But say I have two characters on my account, both miners?

I can gather with Miner A, log off, and get on Miner B no problem and gather. Doesn't matter how many hit in between.

So could you explain your point a little better? Right now you make no sense to me.

Third-edit, 'cause I feel like further explaining:

In your example, you're assuming that the node has a max of 24 strikes, and that people are 'competing' for the strikes. However, the thing you need to understand is, that this isn't the case. Here's how it actually works:

Unspoiled Nodes spawn at specific times throughout the day. For Heavensward Unspoiled Nodes, this is for an Hour-long (Eorzean Time) period, every 12 eorzean hours (roughly 30 minutes.) During this period, everyone with a Miner of the appropriate level can go up to this node, and access it. Depending on your stats, you'll be given a number of strikes to collect ore from it.

So in your example, you said:
2=12 (24)
3=8 (24)
4=6 (24)

However, the way it actually works (and this assumes everyone can get their full 6 strikes; I don't actually know if lower gathering makes it so you can get the minimum [4] on the node)
2=12 (12)
3=18 (18)
4=24 (24)
5=30 (30)
6=36 (36)
^ and the cycle continues on forever. There is never a limit to the node. However, one person can only accumulate so many because of the limited number of strikes, and the fact that once you've used those strikes, the node is gone until the next time it becomes available.

There is no diminishing return per player.