I can't say I really trust central bankers. The incentives on them are to over-expand, and create rising prosperity which reflects on them and their political masters. Often they do not even realise they are doing it. But the trouble is that it takes increasing doses to maintain the high, and when you ease off you get a hangover - and real people lose real wealth. Never mind dashing away the punch bowl - don't serve booze in the first place. Keep the economy sober so people can make rational investment decisions.
When you do eventually crash after the previous excesses, I agree that you need to boost the money supply fast - because just as the banks create money in the upturn, they destroy it equally fast in the downturn, and you have to replace at least part of that to bridge the way from the downbeat to the upbeat without, hopefully, hitting the bottom.
I don't think we have a QE system that actually gets cash where it's needed, though. It goes into assets, which is fine for people with assets, but lesser mortals are left high and dry. In the UK, it basically goes into buying up government debt. But like the rest of us, the government can't get out of a fix just by stacking up more debt.
And then you have to be prepared to take all this money out of the system when things start to turn around so you don't get inflationary pressures building. It might be repressed inflation – where the monetary expansion is actually distorting investment decisions, but people are still too nervous to put up prices. But it is still destructive. Again, there is little incentive on a central bank to restrain itself at this point.
I do worry whether the UK's spectacular recovery is in large part due to all the QE we have done (larger, proportionately, than America's). A recovery built on the same thing that brought us the last boom-bust episode. The trouble is, it's hard to know. You could, of course, rely on the market to tell you, as the market probably has a better collective idea than most monetary officials. But that would mean giving up the monopoly control of money. Central bankers aren't going to volunteer for that (though crypto-currency may do it for them).
Europe's monumentally appalling problems are because they have the same boom-bust problems, but a) a bunch of economies that are state-dominated and fat and under-performing, not the best formula for a recovery, and b) countries that should adjust but are locked into the euro so they can't, and c) a complete inability to take on-time monetary decisions anyway because of all the political differences. Sell your shares in the EU!