I was reading about this last night, and whilst it's not a bad idea in theory, it relies massively on absolute trust within the bubble. Friends or family who live close to one another can socialise together if they all agree not to mix at all with others not in the bubble. They can visit one another, children can play together and so on. At the start of the arrangement, everyone in the bubble has to self-isolate so that everyone knows that everyone else is free of the virus.
If one person breaks that promise, all of the others are, of course, compromised, so all it would take would be someone's daughter to visit from her house miles away, or one of the 'bubble' to accidentally touch someone, and the whole quarantine process would have to start again for everyone. The temptation to overlook small indiscretions would be huge.
Also, how would you feel if all of your friends were in a bubble, but you hadn't been asked to join them? Or if you were in a large family and your grandchildren were in the other side's bubble. I think it could make isolation feel worse for people who end up outside of bubbles for whatever reason, and would be bad for the mental health of a lot of people.