Why do you think that banks will accept Bitcoin in the nearest future? As far as I know, the banks are being careful for now, it is risky to accept something that volatile if the turnover isn't high enough. They declare that it's a
possibility in the future when the demand is high enough. For instance, recently Daniel Pinto, the co-president of JPMorgan stated
If over time an asset class develops that is going to be used by different asset managers and investors, we will have to be involved...The demand isn’t there yet, but I’m sure it will be at some point.
And other banks aren't in a rush towards Bitcoin adoption either. Though, maybe Goldman Sachs will be the first one to take a step forward.