In the long run, holding policy interest rates steady while share or house prices are soaring, in a context of heavy and growing household and corporate debt, could further fuel a speculative bubble that will eventually burst, at a potentially very severe cost to the economy as a whole.
Witness Facebook, Amazon, Google, Alibaba and so on. This is also true within the financial sector, where big banks gain significant economies of scale, leaving smaller banks struggling to compete. This would be fine if it didn’t lead to other problems such as ‘too big to fail’ and excessive risk taking incentives.