Yes, tax competition does pose problems for politicians who buy votes with other people’s money. Tim Worstall points out on the GI site that "if people are able to pay lower tax rates elsewhere then they might just leave and go and do precisely that." Thus the presence of more tax-attractive places restrains the big spenders. More to the point, though, as Tim emphasizes, is that tax competition brings choice and with it the opportunity for people to satisfy different preferences simultaneously.
Some prefer the greater State services (however incompetently delivered) that higher taxation brings, there are even those who prefer greater regulation. Excellent, let those who desire such things have them. And thus the point and value of having competition in such tax and regulatory jurisdictions: people get to choose which they prefer.
Of course tax competition does tend to make one choice more difficult: that of living where there are high levels of state services, but where someone else pays the taxes to sustain them.