I was thinking about this a while ago and I reckon it's quite important that people do look to the government for advice, for two reasons
1. People are stupid
2. A given approach for this sort of thing won't work unless everyone buys in, so you don't want everyone just having their own interpretations of what to do. You don't want to leave things up to interpretation because success isn't dependent on the average interpretation. For example, if the prevailing wisdom is that people stay 2 metres apart and this is offered as a guideline, not a rule, resulting in people staying two metres apart on average, with some staying 2 mm apart and others 200 metres, this will have a worse outcome compared to everyone staying two metres apart.