I think the only real "benefit" in mandating face coverings in outdoor public places is a when local restrictions are needed.
That benefit would be something to the effect of: We need to be seen to be doing something.
TBH I'm of the view that most of what they're doing falls into this category, particularly as some people think they were late on the lockdown bandwagon.
If the government were going to go down the lockdown route then it is beyond doubt they were late into it, though it must be emphasised I have never been a supporter of it. I have said right from the start the boot should have been on the other foot, protect and isolate the vulnerable (esp hospitals and care homes) and everyone else just get on with life as normal. Nothing has happened to change my mind that that would have been the right course, in fact I'm more sure than ever.
Local restrictions shouldn't be used, I doubt they achieve anything significant. I think we're way past the stage where any significant lockdowns / social distancing / quarantine achieves anything much at all, particularly when their social and economic cost is factored in*. But, of course, it isn't being factored in, the world is myopic (apart from Sweden), this is the biggest over reaction in the history of the world..
* If we were in NZ or Australia (and there was hope for a vaccine) maybe, but we're not.