Eothain is a pretty decent ally. His cost is pretty steep at 4, but he will often pay off in the long run when placed in a Rohan deck. We must also consider his sphere match for Steward of Gondor as well as the likelihood of playing Théoden when talking about his cost. This smooths out pretty well after those.
I think its unlikely and uncessessary to put more than 2 copies of him on a deck. He's simply not that essential. However, he can be a game changer if he's given some attention. He is likely to ready often in a typical Rohan deck which allows him to use his 2 and 2 often. Because discarding is expected and can be done for other reasons in a Rohan deck this ends up being a passive ability with great impact. We all know the importance of action advantage. Think Ride to Ruin or Westfold Horse-Breaker, etc combos. He is also in sphere for Gúthwinë which pretty much guarentees you getting a discarded ally back. So his ability will, and should, be triggered often.
So he can quest and attack well. That is not all though. His "warrior" trait lends him to great restricted and non-restricted attachments to boost him even more. Think Raiment of War for defending and attacking both in a round. You can even add Hauberk of Mail on him there. It's a big investment for a 3-4 cost ally but again, it may just be work it in the right scenario. Especially if you haven't drawn into your Warden of Helm's Deep yet.
One final point: he makes a decent Messenger of the King hero. He has better starting than Théodred, the same attack/defense, and the same threat cost. He can be boosted in the same way Theodred can as well. Because of the Steward of Gondor sphere match you could argue the upfront is better for the early game. This is all based on need, though. You just have to outweigh action advantage or resource acceleration (which can be obtained anyway).
So, Eothain probably not a "must-include" 3x copy ally. Depsite this he's still quite useful when given some attention - and I often do sense he is overlooked. He also has a place as a MotK candidate. Give him a try!