It's always a race to the bottom. Smaller countries (e.g. Ireland, Luxembourg, Malta, Cyprus) need a less broader tax base to cover their outgoings and thus will always be able to offer a low tax base. As a (larger) country, you can decide not to participate, but you'd be pricing yourself out of the market.

Imo, it's smarter to tax shareholders more, and corporations less. Corporations are generally productive and having the statutory seat of a multinational company in your country leads to an increase of tax revenue, because 1) people will have jobs, 2) those people will pay income tax, sales tax, will spend at (mainly local) businesses whose shareholders will be taxed, etc.

Dividend and capital gain taxes are generally also harder to avoid for the wealthy. At best you can defer them, so you'll always have to pay some tax if you want to spend $1-2-5m a year. Corporate taxes and income taxes are (very) easy to avoid.

I wonder how much it would cost to completely eliminate corporate taxes but increase dividend and capital gain taxes to say, 35-40%. Now, that said, I don't think this will ever happen. People in power love their tax breaks too much.