Why there is no FPTAS for multiple knapsack problem for two knapsacks unless P=NP?
There is no guarantee that the packing algorithm you suggested will lead to an optimal packing. Say you have two knapsacks of capacity 5, and objects of size 1, 2, 3 and 4. An optimal packing would be putting 1 and 4 into knapsack 1, and 2 and 3 into the other knapsack (switching the indexes on the knapsacks would also be another alternative solution and this is a further complication). The greedy algorithm you have given would not result in this packing.