There's just something thoroughly off about it in my head.
The main problem is that if one could magic up money at any time without any cost, we would all do it all the time. For the same reason perpetual motion doesn't exist, neither can free money.
I don't think they could/would do it all the time as then the (hyper)inflation you talked about would probably happen.
To change the subject a little -- Brexit...
Currently, we seem to be heading towards a 'Hard Brexit' (exiting the single market etc.) I'm not sure what to think about it, but I do think that the issue of the EU for our country can only be put to bed if we no longer have free movement.