Would I be correct to expect that in the (perhaps near) future a global standard will emerge? If so is there any of the current conventions a good candidate for a global standard?
It is a detail that is important to get right, but otherwise uninteresting. There is no point in changing a convention once you've set one. There are some more common ones associated with the biggest markets, like Act/360, but that's all.
Day count conventions are well documented. There is a degree of consolidation via ISDA standard contracts in the IRS market, but it is limited.