Well just my little bit as another Sheffield cyclist commuting to work most days, yes I think it's your plumber's fault and I suppose he can expect a claim - surely we do all check before opening our doors.....?
Should the cyclist have allowed clearance around the door?
Yes there's definitely an argument there but in my experience not really practical on the road where other users are doing their best to crowd you out.
Should cyclists pay road tax?
I don't see a great case for this, cyclists do little significant damage / wear to roads and are probably already contributing via other taxes. I'm personally already paying road tax through my car, I'm sure you won't begrudge me a little cycle use on the back of that.
Should cyclists be (third party) insured? Actually I think they should, tho' I don't know how to enforce it. Wouldn't cost a lot for the cyclist and would be protection for them too, especially if it included a legal insurance policy to recover damages caused to cyclists through injury.
Sadly there's a lot of conflict between cyclists and other road users.
I'll admit to a few red mist moments on the bike - being pushed around / threatened by cars tends to cause a big rush of adrenalin which can easily be converted to aggression - I'm trying very hard not to rise to it these days!!