Unfortunately, Linden has chosen to hide her intention to resurrect Covenant from her companions, and the author has similarly chosen to hide them from us. So we can't really see exactly what the author says about her motivation.
However, it is entirely fair to extrapolate from her character as it has been established, to let her past actions be a guide in deciding how to interpret this one.
In the story so far, we have not seen Linden acting impulsively or irrationally since coming to the Land. Lord Foul has her son, and innumerable god-like enigmas have come out of the woodwork to make her feel small and incompetent. But despite being pushed in these ways, she's made plans and stuck to them.
First, she's done everything she could to understand the situation. She's questioned Anele, the Masters, Esmer, the Mahdoubt ... everyone who seems to know what is going on.
Second, she's done everything she could to gain allies. The Ramen. The Ranyhyn. The urviles and the Waynhim. Giants. Even the Masters.
Third, she's done everything she could do to gain power. The ring, the Staff, and the krill. Even the Ranyhyn and urviles are a signicant power, because of their ability to help control
ceasures.
And she's done all of these things BEFORE attempting to rescue her son. Before trying to save the Land. This is not an emotional or irrational response. This is a plan.
You say that she has alternatives. I don't see them. And in fact, I don't even think it is pertinant. She's smart enough to know that she needs to get EVERYTHING that she can get before she faces Foul. She's not picking and choosing from her available options, she's taking them all.
If we extrapolate to this case, we can easily argue that she's chosen to resurrect Covenant because he has knowledge that she needs, and because she needs allies, and because she needs power. Covenant represents power, at least because she feels like she can't use the ring as effectively as she wants to.
Sure, she loves Covenant, and she misses him. Sure, that means that there is a personal side to this decision. But its easy to see that these are side issues, and that she has a valid, well thought out plan for bringing Covenant into the story.
[Edit]Malik, you can't argue that the Staff was unnecessary if she was resurrecting Covenant. Because she needed the Staff to do that. Even if she has no further use for the Staff, that one act was sufficient to justify acquiring it.
As I said, I think she's trying to load for bear. She's not picking which weapons to use, she's loading up with ALL of them.
As long as she has the Staff, she has the option to operate as "a sniper", even if she has an "atomic bomb" at her disposal. Options are good, more options are better, all options are best. Covenant may be "da bomb"

but that doesn't make the Staff acedemic.