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Who said that it "has to be bigger than the first stage?"
Please, provide me what books/references that put so strong affirmation.
Of course, everything depends on what kind of application your aiming for.
There are a lot of reasons you want to burn more current at the output stage: increase the overall open-loop gain, give enough current to drive your load, reduce slew-rate, reduce noise, increase speed, improve linearity, bla bla bla.
And regarding your second question, you should provide us more information to answer this question accordingly.
What is your application? What is your load? What is the value of gain that you need? What is the required speed? ..... ?
Depending on your application, and the technology you are using, of course you can put whatever current at the output stage - as long as this enough to meet your specs/application.
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