If used to address systemic risks, it may unnecessarily lead to recessions that inflation conditions would not justify. This is even more the case in a monetary union where vulnerabilities identified in each country can be addressed with macroprudential policy, allowing for the appropriate heterogeneity, while countries remain subject to a single monetary policy.
Another aspect of the problem is that when asset returns are going up sharply, for instance in housing, the increase in interest rates would have to be quite sizeable to have any effect in curbing an asset price boom.