(Or is there a some economic reason this is a terrible idea?)
Adopting another currency makes sense if it's easy to do a lot of trade using it. The closer you are to other $ users then, the closer the real value, because you can easily trade outside of the local bubble.
(It could work of course (and did for some countries)... but you still need to have actual well working trade to make sure the currency has the value you expect)
The point of pegging your currency to a foreign currency is to rebuild trust in your currency by guaranteeing a fixed exchange rate.
But if you do that by pegging to multiple currencies that all have variable exchange rates, how do you handle the relative changes between them ?
The only way would to be adjust it almost daily. Which is the same thing as letting it float.
++ PS: I'm talking about a somehow hard peg here. Most countries tend to use targets and will try to maintain some levels of rate. But they do so by operation on the market rather a peg by fiat.