But, let's say that the current VAT for a given type of product in a given country is 20%. Is it illegal that I, as a company, charge 5% only (or even 0%)? Sure, I understand that I, as a company, will pay the difference to the tax system anyway.
Why would I do it? Well, mainly because staying up-to-date to how VAT changes across different countries is a PITA. I know that there are companies that provide this kind of services (VAT related), but let's imagine that I want to keep my company as independent as possible of external factors and that losing VAT money, in my opinion, is worth it if that means I don't have to worry about VAT anymore.
My two cents is that you are the one paying VAT to whichever government your business is obliged to pay VAT to. Even if you calculate your prices without VAT you will still need to 20% owed according to your example.
So if you only add a surplus of 5% for VAT the extra 15% would come out of your product price.
I would choose a payment processor that applies the right kind of VAT according to where your buyers are located and have that data directly fed to my accountant. Then you can be sure your are not loosing money to taxes and that your are following the law to the best of your abilities.
You still would have to know how much to pay and have to be able to prove to the tax department how much you have to pay, which means tracking how much value your company added, which means tracking all your sales. Adding an amount you already have to compute and store to each bill wouldn’t be The problem.
(I’m not a lawyer, certainly not one who happens to know what VAT looks like everywhere in the world)