However, is it not unrealistic to have the government control
trade in any government other than a Despotism/Monarchy/Communism?

I propose this: when you are in Republic/Democracy/Fundamentalism
you lose the trade option but gain a new one: ACQUIRE. The ACQUIRE
button would allow you to recover silks and such that the trade caravans
have acquired. When the silks and such have been acquired you can outfit your
palace better, but you will no longer have trade income as you would in Despotism/
Monarchy/Communism.

I think that once a trade route is set up there should be a unit that is created that brings the other trade good to the City A. Then when this unit gets to the City A a unit is created to ferry a new supply to the City B. You don't have to control this unit. It tries to find the fastest route to its destination even if it brings it through other cities. The cities that it has to go through probably tax it. You can also tax other units and you can grow fat on other people's money. Also you can play pirate by "killing" another civ's trade unit and getting money from what you got. If you capture a ship than you can take the occupants as hostages and get money for their return (I.E. being a "terrorist" country.)