Is post fit simulation using timing netlists necessary although design meets setup-hold time requirements?
Yes, post-fit timing analysis using timing netlists is necessary, assuming that you really want your design to work.

Remember that all simulations are just an approximation of the actual device behavior. Going through the process of fitting your design can change some of the routing and wiring length, because the tools don't really know how far apart your logic cells are until after they are placed. Hence, the parasitic capacitance and resistance of the wiring can change, leading to changes in propagation delay.

Every step in the design process leads you closer to the final product, so a timing analysis should be performed after each step using delay values that are extracted from the actual design. After every step your timing analysis will become more accurate because it more correctly represents the actual design.

You should always create a testbench that will check whether the design still meets all of its functional requirements. Ideally, the testbench will spit out an error message if the current simulation results differ from the previous simulation results. After every change or improvement in the design you repeat the simulation...this is called regression testing.