The problem with the bail-in is that at the end of the day, if there isn't enough wholesale capital available, depositors are still on the hook. Indeed, we saw the only instance of the bail-in in practice (that I'm aware of at present) so far in Cyprus resulted in depositors having a portion of their savings converted to equity (in a nearly-insolvent entity).
At the end of the day, the risk still lies with the public if things get bad enough at a big bank. Through their deposits, through the FDIC, or through a bail-out, if the political winds blow that way.
The truly safest solution is to separate investment banking from depository banking again and to further limit both the size and the allowable exposure levels of investment banks.
I don't think the bail-in can yet be framed as a good thing. It's theoretically helpful in limited situations where enough wholesale capital is available (or can be made available) to solve a crisis of liquidity. Outside those boundaries, it induces greater risk on depositors. And in that situation, it may actually be good (in a perverse way) that the public doesn't know more about it, because if they did it'd likely increase the incentive/pressure on deposit bank runs.
Again, the solution here is to separate depository banking from investment banking. Or, put another way, to very tightly regulate the sorts of investments that depository banks can make. On top of that investment bank investments should be regulated more than they are today. And on top of all that, continuing with a rapid-insolvency process + bail-in would make sense for both depository and investment banks, should the need ever arise in either case (which likelihood would be greatly reduced through these further regulations). But the bail-in without these other measures carries risk and will be of only limited assistance.