Why do you think Plato felt he could not have a career in government?

Plato contends we are all made of the same three parts yet not all have the parts aligned in a healthy balance. The result is that greed, ambition, and foolishness rule in these unbalanced people. Plato lived through the democratic period in Athens' government and through the oligarchy period when the conquering Spartans installed the wealthy oligarchists as rulers of Athens, a move that unleashed a fierce retribution of bloodshed upon the unseated democratic rulers.

Plato rejected the rule of the mistake prone and seemingly unreasoning democratic faction and equally rejected the oligarchic rule of the retaliatory wealthy elite. After a period of seclusion, Plato wrote the Republic. In it he describes human nature and uses human nature (as he described it) as a metaphor and template for a reasonable government.

He assigns ruling authority to those who have a functioning alignment and balance between their three constituent parts and a dominant dedication to the highest: (1: lowest) love of money (laboring and merchants classes), (2: middle-most class) love of honor (military), and (3: highest) love of wisdom ("scientists, scholars, high-level experts, and similar sophisticates" [Jorn K. Bramann]).

His idea is that the two models he has seen don't work, so a third is needed. That third model is to make a government out of those who have the best minds by virtue of being best trained, best informed and best balanced (in the quote below, take note of and understand the "or"):

Until philosophers are kings, or the kings and princes of this world have the spirit and power of philosophy, ... cities will never have rest from their evils. (Republic)