"Let's eat more rice."
Translation:Comamos más arroz.
The suggestive "Let's [do]" in English uses the command (subjunctive) form of the verb in Spanish. It is definitely not the same as saying "we are going to [do]".
You are saying "We are going to eat more rice" (sometime in the future) which is not exactly the same as "Let's eat more rice" (now). That's just a guess (future phrasal vs. now)
I learned that only the negative imperative needed the subjunctive. Why did I have to use it here?
That is true for the 2nd person familiar. In 1st and 3rd the conjugation for the imperative is usually the same as the subjunctive.
What do you think about: "A comer más arroz." I wrote it and duolingo says it's bad, but I've heard many times "A ver!" for "Let's see!"...
I think "a ver" is merely a shortened form of "vamos a ver" but it's an idiomatic expression and doesn't work for all verbs. As was commented above, using "ir + a" construction is not the same thing as the command form. "Vamos a comer" = we are going to eat; "comamos" = let's eat