Also, if someone can break sha256, not only is bitcoin screwed, but so is the Internet as we know it and every secure institution period. The overnight "instant and complete" breakage of fundamental assumptions about security would destroy everything. So interestingly, if you could break sha256, you could probably break into almost any financial institution and steal their money as well.
The security of a blockchain is in its popularity. As long as the code is open (and I'll admit, I am not a fan of how bitcoin mixes the default interface (BitcoinQt) and the default implementation (BitcoinCore) together so much) and there is investment in the market, there will be strong financial pressure to consistently and diligently analyze and track the source code for weaknesses.
Bitcoin at 3B has at least a dozen security firms that have looked into its crypto. If you had another crypto that broke a trillion you would have thousands of companies constantly safeguarding and testing the crypto of the currency in the same way Google offers ludicrously high bounties for anyone who can break Android/Chrome/ium security.