If Mary is born with a sin nature according to the Orthodox, then my discussion is not with them.
The point remains for those who do accept that she was born without sin and that she did not sin.
Since Jesus, the Lamb of God, paid for the sins of the entire world, then there was nothing preventing Mary from being assumed into heaven. The assumption is Catholic teaching, therefore, it is consistent. They had to have her assumed since they had her entirely sin free.
The only reason Jesus died was because He took upon himself the sin of the entire. That task being accomplished, there was no reason for Mary to die which is the penalty for sin. (The wages of sin is death...)
I never said we believe that she sinned. She was born fully human, like any one of us, with fallen human nature that desires (i.e. has propensity) to sin.
But we hold that she never did sin, not because she was somehow superhuman, but because she was bale to love God more completely than others. Which is why God, in his foreknowledge, chose her, as the suitable immaculate vessel, and a blameless Mother of God.
Because our nature is mortal, as a result of ancestral sin of Adam and Eve, Mary died like any other human being, even if she did not sin. Her nature was still mortal.
The assumption is Catholic teaching, therefore, it is consistent
Not really, not Roman Catholic. As far as we can go back into Orthodoxy, the East always mantained that she died and was assumed into heaven on the third day. The Catholic Church did not make it a dogma until 1950.