Well, that is the thing, I am not sure if having a larger pond, and of course missing trees around it, would be a good or bad thing. There is enough room to let the pond get bigger, but I never dealt with beavers before, do they keep chomping trees even after the dam is built, or is it a constant thing. I haven't made it to where their dam is yet, but it looks like they may of been there for a minute, so it may just be done, or about done. Also, how bad are they on the fish, because I would rather have a bunch of fish and less beavers.
Again, I will admit to bias toward, "let nature be nature." And of course, if the beavers continue to live there, they will continue to feed. But not nearly to the degree as when they are dam building.
To my knowledge beavers have zero direct impact on fish. If anything, a larger pond creates more quality fish habitat and most likely more fish.
The damaged tree pic you posted above is not a mast producer, so I see no problem (for deer) in its loss. And opening up thick forest canopy encourages more growth of browse species, which obviously deer do depend on much of the year. So again, unless they are flooding a huge percentage of whatever size parcel you have, or if they are damaging a significant amount of mast-producing timber... or timber you want for future lumber production, I see no problem.
Also, if it is prime beaver territory, it will be a never-ending battle trying to keep them out. Even if you are successful in trapping out an entire family group (which is difficult), there is a good chance a new group will move in and begin the process all over again.
My two cents worth. In the end it's your land and your call. If you decide to attempt eradication, just be prepared to "do the work." They are persistent little bastards.