Deciding that the other sheep have been being called right alongside the anointed since the first century would relieve them of a lot of doctrinal problems...
I think this would resolve some problems, but it could create others.
Christians aren't supposed to serve god for a reward, but salvation is still an integral part of Christianity. Allowing for the existence of "other sheep" who are not also members of the "great crowed" in the Christian era creates a third group of Christians who do not attain to the salvation that the JW's believe Revelation describes for the other two groups.. --In the language of Revelation, this third group would neither sing the "new song" on mount Zion nor would they wave palm branches before the throne and shout.
What would be the difference between a Christian with the earthly hope and a non-Christian? For example, in practical terms, what would be the difference between a Christian with the "earthly hope" who experienced a violent end in a Roman arena and a non-Christian? As far as their final destiny is concerned, none. The JW's believe there will be an earthly resurrection of both the righteous and the unrighteous. So why be a Christian at all?
For that matter, what would be the difference between a JW, who died faithful in a concentration camp and someone else who never bothered to become a JW at all, avoided imprisonment in the death camps and lived a long and happy life? If the JW had the "earthly hope" there is no difference. Both individuals will be resurrected to life on earth.
Currently, very few JW's actually think about such things, but deciding that the other sheep have been called since the first century will call attention to it.