World wide wi-fi

Sure I can go into a coffee shop or an internet cafe to get access if one is available, but it’s a hassle as you often have to ‘register’. Why should it be left to businesses to provide internet access to the masses? Wouldn’t it be in any nations’ interest nowadays to ensure that business can be conducted in an efficient manner at all times in as many public locations as possible? Especially when so many people travel a great deal as part of their work. A centrally run system would mean you wouldn’t have to enter passwords each time you change location. More and more software products are going cloud based, and more and more services that would once have been freely available on any high street are becoming the sole domain of the Internet, so isn’t it even more important that we have good access to it?
I kind of feel that the government should ensure that such a system is available not just in the UK, but also work with other governments across Europe and beyond. It doesn’t have to be government funded, but I do feel the goverment should take the initiative. I’m sure also that existing coffee shops, hotels and other wi-fi providers across the country could be subsidised for contributing (acting as access portals) to such a scheme.
There may be a million and one reasons why this would be an awful idea, and I’m happy to be wrong, but just just wondered if anyone else thought the same thing?