Erythrocytes- Why do they work so well with no nucleus?

They work so well BECAUSE they don´t have nor nuclei and neither mitochondria.
Without nuclei, red blood cells don´t synthesise proteins, or other large energy requiring process. So, they don´t need large production of ATP, that would occur through the respiratory chain.
One of their functions is to transport O2 in the hemoglobins from the lungs to the other cells, so these aerobic cells can use this O2 to transform electron energy into ATP energy (through the respiratory chain which is located in the mitochondria inner membrane), useful form to do work.
Without mitochondria, all the transported O2 reaches the aerobic cells.
Without nuclei and mitochondria, erythrocytes are small and acquire their optimum hydrodynamic form, that allows them to flow pass through the very small vessels and to get very near the cells membranes and thus exchange O2/CO2.
So, it is perfect for its function! As are all the cells.
I would say that mature erythrocytes are DERIVED from complete cells, and during the maturation cells the organelles are destroyed. O. K. ?

All mammalian RBCs are denucleated. This allows them to carry more amount of OXYGEN which is their Primary function.
AN RBC doesnt need NUCLEUS coz HAEMOGLOBIN SERVES THE PURPOSE.

Lack of nucleus allows them to carry more gases.
Because they are atypical cells, sometimes the're referred to as "corpuscles".