This a question “How Strong is Strong Enough?” that has been asked many times by some really smart guys and the answer is: NO ONE REALLY KNOWS.
Something important that is easy to over look: Athletes don’t use strength training just to get stronger. They use strength training as tool to help them perform better. It is very easy to get caught up in the gym culture of just lifting heavier and heavier weights when that excess strength may have no positive performance benefits and may even reduce performance. See the Dead Lift comment below.
We know that even for endurance sports some minimal level of strength is needed but how much no one can say. Is basic or general strength important for performance or is it only important for injury prevention? We can be pretty sure that sport specific strength more important than general strength.
General vs Specific
Being able to do a one arm pull demonstrates very high general upper body strength but up is no guarantee that one will be a better climber. But being able to hang full body weight off a 1cm edge for 30 seconds will correlate well with climbing ability. Being able to deadlift 2xBW shows good general leg and core strength but probably correlates poorly with running performance. In fact DL max probably has a negative correlation with running performance after about 1xBW. But horizontal distance covered by 10 single leg hopes correlates very well with running performance.
The strength programs we prescribe in TftNA and in many of our training plans are basic or general or in some cases like the box step up, semi sport-specific in that it closely mimics the joint angles and contraction speeds of hiking steeply up hill. In the Specific period for any sport it is important to convert this general strength into the type of strength quality that your event demands. For most mountain sports that quality will be muscular endurance. For a boulderer that quality would be power. Converting general strength to sport specific strength is critical for the best performance.
In your case it definitely sounds like you have excessive general strength for your event. Mountain endurance athletes really do not need to be very strong. Lets take the box step as a test for mountaineers as an example: As we mentioned in our book, if you can’t step up on to a 12 inch high box even one time with the weight you will be carrying on your climb then clearly your strength is too low because you will have to do this thousands of time on the mountain. But if you can step on the box while carrying, say 50% of your body weight, then you have more than adequate strength and need to focus on converting that to muscular endurance.
I have worked with a few people with very strong legs who, like you, could not reach local muscular fatigue when hiking uphill with a heavy weight. Like you they had an imbalance where their aerobic system need a lot more development. My suggestion for them is to stop doing max strength work and spend that time doing more aerobic work in a sport specific way (hiking uphill without added weight in Z1-2).