The problem with profit taxes is exactly as you say, but VAT is paid in the country where the consumers live (at least in the EU). This means VAT simple adds to the purchase price, which the company doesn't really feel and ends up basically being the consumer's problem, while the costs and profits are manipulated and moved around so that the company has to pay as little tax on them as possible.
If profit taxes were treated the way VAT is, so the company would have to pay them in the country where they made that profit, which means the revenue in that country minus the costs in that country, that would stop companies from moving their profits around, because they'd have to pay them in the country where they sold their products. And it would make it attractive to make their costs in that country too, rather than outsourcing them to tax havens and low-wage countries.
Maybe I'm misunderstanding you, but that's kind of how taxes work now. You report your revenue and expenses and pay taxes on the difference.
The challenge is that there are so many loopholes that some companies can reduce their profit to 0 (or less) or allocate their profits to lower tax regions (Delaware).
A revenue tax would be far simpler and eliminate a lot of these accounting loopholes.
For maximum ease, have the banks automatically deduct 5% of each deposit and don't worry about even having to file taxes unless you received cash.