Squats and leg presses= improved climbing.
While they may keep your over all fitness level up and of course that helps it may not be the best training for cycling . I looked into jogging for training for my TT's and was told it was pointless as they are not the same muscle group to build up my legs . Breathing wise I think jogging would benefit my cycling but I'm happy with thinking its pointless
Since I have started TT's I have ridden a lot less than I used too . The rides I do are mainly at flat out pace and my times have come down over 10 miles by about four minutes .
Riding less is due to work and its annoyed me but that's life . What it has done is shown me that with very little training but training aimed at your maximum effort works .
You can only do max effort if your body can get the oxygen you need to move the blood to the muscles .
That's my take on it anyway .