First of all, the 6080 is running as a cathode follower, so its gain is in fact slightly negative. Secondly, sure, you can build an amp with any gain you want. But how it works with other gear may be very unpredictable. If there is a generally accepted range for the gain of each component in the chain it becomes possible to design the circuits in such a way that the noise floor of one component doesn't get amplified by the next one so much as to intrude in the music. The 12AU7 has plenty of gain for the application. More gain isn't impossible to use, but it doesn't necessarily make anything better and might create a noise problem.
The power transformer current rating has nothing to do with the gain structure.