Nothing. Bitcoin isn't a POS coin and right now there is no way to force through your will by abusing the power that holding such large number of coins do.

It could potentially be abused in case the developers suddenly want people to vote with their coins to approve or reject certain proposals, but that with a high probability will never happen. On top of that, Coinbase has its 'majestic' reputation at stake; one wrong move with people's funds and they may regret it for ever.

It will be interesting to see what happens when Ethereum switches to POS though, because Coinbase's Eth holdings are just as dizzying as their Bitcoin holdings. Perhaps that people will be incentivized to take care of starage themselves.