When competition between companies lowers the cost of goods and services, that's considered to be a good thing; why is it considered a bad thing when competition between governments lowers tax rates? Lots of governments look like they could use a good dose of efficiency to me; more government services for less taxation.

It's not the rates. The point of the double Irish is that companies avoid paying even the low rate of corporation tax by assigning IP to shell companies that don't actually do anything except lease it back to the parent company so it can be booked as a tax-deductible 'expense.'