For most income earners, defining money as income is easy and taxing it is easy. For high income earners, it is not. Is this a revenue, profit, personal income, capital gains, etc? Capital is mobile, you're right. So are cash flows from that capital. A lot of that is for reasons to do with legal structures: jurisdictions, corporate law, etc. It's hard stuff to change, especially if your goal is "raise more tax next year."
This is why the upper middle classes pay so much tax. They're easy to tax.
Anyway, I agree with you to a certain extent. It's hard to tax capital gains, or other incomes that are not "salary from job X." But, I don't think the "improves the lives of those at the bottom" argument holds water at all. So is "Labour" and so is "Natural Resources" or any other economic fundamental.