Written from the British context:

Should the system be changed to one where companies are taxed on all the profits they make from their sales in the country?

There are a few downsides to this.

First of all it would be very hard for one country to switch to such a system without getting the rest of the world to do it too. If we did it unilaterally it would open up more differences between national tax regimes and so create, rather than reduce tax avoidance loopholes.

It is also far from clear the UK would gain from such a change. We might gain from some of the big US-based multinationals paying more tax here, but we have plenty of multinationals of our own and they would generally end up paying less here. The biggest losers could well be poorer developing countries, especially those reliant on extractive industries such as mining. If they could only tax companies based on their sales to their residents in that country that would bring in a lot less than taxing them on the share of the economic value of the products generated in that country. The UK itself still generates between 8 and 9 percent of Government revenues from corporation tax, which is pretty respectable internationally, despite being a very open economy exposed to competition.

There is also an economic question as to who ultimately bears the burden of taxes ‎on a company - is it the shareholders, the customers, or the workers, and if the workers, is it the highly-paid top management or the people at the bottom? The answer is not certain, but it does seem likely that a shift to sales-based tax would be at the expense of the customers. In other words, by taxing internet-based suppliers more, we could be more heavily taxing ourselves.

But the strongest argument against is fairness. If a product is invented / developed / mined / refined / built and potentially even marketed and sold all round the world entirely from country X, making use of staff educated in country X, who use country X's health care system and transport network, often with tax breaks from country X to encourage its growth, and maybe even wage subsidies from country X for its employees, who deserves to be able to tax the company's profits? Is it country X, or every country that has someone in it who buys a product from the company? Of course if a country wants to tax sales it can, and sales taxes such as VAT are a perfectly reasonable and sensible part of a country's tax mix; though in the EU, this is governed to a considerable extent by EU rules.

There are many further detailed points at the link.  And do note this:

There is a perceived issue with the internet making it easier than ever for companies to 'sell into' a country with little or no presence in that country, and therefore offering little or no taxable base for the government of that country to tax the profits of. Sales taxes can be part of the answer to this.

But of course a sales tax does not appear to consumers to be a free lunch, and so it is not as politically popular as a sales-based hike in corporate rates.  And so we arrive at the current mess of a situation: "We want tax equity, but you can't possibly expect us to do that in a way that is transparent!"