I guess the question is will removing the mistletoe help to re-establish vigor all other things being equal and relative.
If not, then there would be an underlying primary causal factor. Tree pick there environments to thrive in. That falls under the "all things being equal and relative". Species have their precise lattitudes and temperate zones.
Therefore, mistletoe on trees in arid vs. humid environments would most likely attack under similar conditions. A healthy or declining tree in both environments would be relative to that environment. The mistletoe would take advantage then of the stress the tree is under, unable to protect itself and less vigorous (in whichever environment it is in).
The oldest living tree (Bristle Cone Pine) is found in the Mojave desert. Temperature and humidity don't factor into success. The tree has filled a niche, and thrives there. When it gets stressed, it declines and is more likely to succumb to an outside parasitic, viral, environmental or mechanical injury.
I would have to go with a scientific study that indicates no causality toward the mistletoe, and question why funding would be used to attempt erradication. Is this for lumber harvesting? Is it that we are down to less than 10% of old growth and attempting to maximize production and quality in the shortest time? Is it a factor that production has created, and then spread into our urban settings? Why would there be such a move to "eradicate mistletoe".
I wonder how much funding is behind this, and more importantly, where it is coming from. Maybe someone can look that one up.