I think having 1000 notes is a bix extreme and they must be a big target for counterfeiters but I can't imagine many places accept them. In my country most shops wont accept 50 notes because of the chance of them being counterfeit. In fact it is very rare to see them at all and I have only ever see a couple in my lifetime. Trying to ban them just because criminals use them is sill though but maybe we should ban banks too since they're the biggest criminals.
If you have read the posts after your reply, you might have already seen that this contention is quite dubious and shaky. It may indeed be true that counterfeiters aim for the larger denominations of the same currency, but, as it has been revealed, this can be easily overcome by implementing state of the art anti-counterfeiting measures. The 1,000 Swiss frank banknote has the largest denomination as well as purchasing power among major monies out there, but it is 5 times less likely to be counterfeited than the 500 Euro banknote, second in purchasing power. The latter is still less likely to be faked than the 100 US dollar bill, which comes next in purchasing power...
Thereby, given the global nature of today's world, counterfeiters should necessarily aim for the weakest currency (in terms of protection), not the largest denomination (purchasing power) between monies