Competition is seen a good thing because it leads to better products or services, with the crappest going out of business. 99% of people benefit, with the remaining 1% being the employees of the organisation that went out of business.
What you a describing as "competition in tax regimes" is in fact companies being resident in a country defrauding that country of the amount required to maintain infrastructure such as schools and hospitals. If done on a wide scale, this leads to that infrastructure collapsing. This is generally considered as being undesirable, especially by the people living in those countries.