There will be mortals and immortals (ie resurrected in Christ ruling and reigning with Him) in the Millenium.
Remember they talk about the man who died at 100 during this time and people will say he died so young.
besides at the end of the Millenium Satan leads a final rebellion, who do you think will side with Him? Not the resurrected in Christ.
There are many things related to the New Covenant which were secured by the work of Christ on the Cross, by the shedding of His sinless Blood.
When someone says that healing of our physical bodies was provided for in the sacrifice of the Saviour, that is true, and obvious. But it does not necessarily mean that all things provided-for are guaranteed immediately.
There are land promises, as well as regal promises to Israel (Abraham's physical seed) provided-for in the sacrifice of Christ, included in the New Covenant. But these things will not be realized until after the removal of the Body of Christ.
The removal of the curse (Genesis 3) is provided for in the Blood-shedding and resurrection of Christ. But the curse is NOT removed yet, and will not be removed until the Second Advent of Christ.
One of the reasons our physical bodies are sick is because of the curse on the earth, preventing plant life from yielding its full product that would give our food supply the preventatives to disease that we need. Crops and wild foods will not yield their fullness until the curse is removed.
Our Lord certainly does heal very often in direct response to the prayers of His people. He certainly has the power to do so, and the prerogative to do so.
But to say that God does not want us sick goes beyond the Scriptures and denies another prerogative of His, and that is to use physical infirmity to teach us His grace, and teach us that it is sufficient (2 Corinthians ch. 12). It also denies His prerogative to use physical illness in the discipline of His children (1 Corinthians ch. 11 ; Hebrews ch. 12).