It's a little more complicated than that. For one thing, if you tax based on number of employees, the employers who can will stop hiring people in jurisdictions with higher taxes. Which is the opposite of what those jurisdictions want, so they won't want to tax based on that.
But more than that, it doesn't really work: How do you define a corporation? If a holding company in Bermuda owns the US R&D outfit, and you tax based on the profits of the US R&D subsidiary, the executives will arrange for the subsidiary to make minimal profits and the holding company or another subsidiary to make more profits. Conversely, if you tax based on the entire conglomerate, they stick some labor-intensive manufacturing company into the conglomerate which employees a hundred thousand people in some third world country, which dilutes the 5000 US employees doing R&D into nothing.
The problem is that there is almost no industry where profit margins are so massive that they can't be completely consumed by systematically but only ever so slightly overpaying for everything, and buying it from subsidiaries in other jurisdictions who end up reporting profits there, where taxes are lower.
There is really only one way to prevent this. You tax based on revenue rather than profit, so that "transfer pricing" doesn't matter. But revenue taxes are very silly unless it's a VAT, since otherwise you get tax paid on tax and it compounds based on the (extremely arbitrary) number of transactions that occur, which highly favors extremely vertically integrated companies.
So you're really left with a VAT instead of an income tax. Which is probably not a bad idea, if you combine it with a yearly refund in a fixed amount per taxpayer to make it progressive.