This is the only situation I know, where a company distributes their product for free and then asks everybody to pay for it. This is a special situation of course, because the public broadcasting has the official task to educate and report in a neutral way. This is welcome - no doubt.
But the presence in the internet and thus on computers is no excuse to collect money from everybody. In contrary, the presence of the internet allows to measure exactly, who is using the services. In a few years from now, perhaps even today, it would be possible to do the same with the wireless receivers, like TV.
So it would be easy to charge the households who use the service. No GEZ needed any more, but a fair system that charges for usage.