No we do not. Tax harmonization is being aggressively pushed by certain member states for their own benefit and to the detriment of other, less developed member states.
To steal from other EU members is no competition it's just unethical. Small countries can live just by cashing a small part of the money that is rightly owned by countries with more population. That needs to be fixed.
Also obviously the EU can put in place any kind of controls it deems necessary on the common market. It’s sovereign in this matter after all and tax dumping is mostly helping foreign-based multinational corporations.