I haven't seen a 2000 yen bill since 2009 or 2010.
On many levels they are like the dollar coins - there, but completely annoying. If you have 1000 yen 10000 yen bills in your wallet, a 2000 yen bill very easily becomes something handed over with some 1000 yen bills (with you forgetting it is a 2000 yen bill), and the cashier not noticing as well.
My fiance and her mom visited the US and I went with. They were confused about the change (yeah, a dime doesn't say ten cents on it) and got some dollar coins - I made sure to use those ASAP.