If you would be able to go backwards with a real aircraft you wouldn't need pushback when leaving the gate. If you could go backwards with reverse thrust, the airport terminal would be noisy whenever a aircraft would leave the gate.
There are planes that can and at some places use reverse thrust departing from gate. Aircraft like ATR-72, Saab 340 do this very often. Can also be done in DC-9, MD-80 etc. This is called a powerback, or powerpushback instead of pushback.
(Power)pushback = gate departure using own engines.
However, in reverse thrust the jet blast is directed to forward. It is not very much used for gate departure because the jet blast is directed directly towards the terminal windows.
1740 days idle. Beat that.