It doesn't make much sense unless you are going to use them on something else besides trading (which is simply impossible right now in any significant amount). Otherwise you inflict uninvited costs on yourself. Central banks are doing this because they have to defend their exports (as an example). They don't do it just for the sake of keeping exchange rate at certain level...
If you mine bitcoin, you will be able to see things from the view of a central banker, since you issue money. It is very easy to understand why banks do this and do that if you issue money by yourself...
The first priority is always keep the value of their money stable, all the other things like full employment/price stability/international trade deficit are all trivial things compared to the value of their money. That's the reason they'd rather close their pocket and see people suffering instead of open their pocket and let inflation quickly destroy the value of their money
The problem with such logic is that it is not only you who mines bitcoins. Though a feeling of being involved at issuing "money" can inflate one's ego somewhat, I doubt it will be enough to actually go and try to stabilize bitcoin exchange value (since you would inevitably incur losses on yourself). If what you say were true, it would have been done so long ago by those who have big wallets. If they haven't already done this, why should they do it right now or later?