Tripodium are not commonly used by classical guitarists at this time. Most performers stick with a simple foot stool. What you have to remember is that in Aguado's (and indeed Carcassi's) time it was equally likely that you would be playing with bare fingers, than your finger nails. In fact, even in the 20th century using your nails was somewhat controversial:
As nearly all classical guitarists today use their fingernails, the extra projection from the special stand is often not needed. I needn't mention the modern convenience of microphones. Also, notice how much smaller the guitars of those times were. Certainly not the booming concert hall instruments we have today, but something more closely associated with intimate performances.
However, I'm sure some modern revivalists would love to use a Tripodium. If you are interested, you should build one yourself - it will be sure to turn heads, especially at a baroque music society.
Oh, and last of all, yes, guitarists do use a special stand to play multiple guitars:
To my knowledge they have always been called gracie stands. They don't have anything to do with projection, or at least in the intended rock concert setting there is little point in that facet of their construction. Rather, they just make it easier to stand up and play or two guitars.