It severely reduces their ability to attract future business, as well as the likelihood that companies will continue to remain headquartered there. If you go there for tax benefits and those tax benefits go away, how likely are you to continue to bother with such complex structures?

At a certain point, where you have such different views in countries like Hungary (Hungary wants to placate Russia or something similar leading to not helping Ukraine, wants to block Finland and Sweden from Nato, wants to disable/reduce/destroy democracy in Hungary, wants all that stimulus money from the EU to keep coming in), we just have to say we'll go our way, you go yours. Unity required for so many decisions means the extreme minority of 1 can extract too much. Similar thing for Turkey and Nato.

Either that, or the groups (EU, NATO) will have to change their rules to allow a few no votes on things, or they'll just become broken orgs. I'm sure Russia would offer almost anything to the wanna-be dictators in Turkey and Hungary to get them to vote no on these things. These "complete agreement" democratic groups don't work when some leaders are dictators.

This is empirically not always true. Higher taxes can lead to lower tax revenues if it reduces the size of the pie when business go to tax friendly jurisdictions.

This can also work with income taxes. For example if you set income tax at 100%, you'd get 0 revenue probably because no one would work. This effect happens at values below 100%

Why do countries have lower tax rates to start with?

For many small/remote countries, lower corporation tax is a way to attract companies that would never have come if the tax rate was higher.