I think signing an actual contract marriage should be no different to registering a birth or death, and people can knock themselves out and do what they want after that.
You mean, "go to a registry office, sign a piece of paper, attest to its accuracy, leave?" Does anyone disagree? The claim that the requirement to find two witnesses, who can be staff at the registry office, is a major barrier to marriage is being made in bad faith: no-one actually wanting to marry is stopped by the need to have a couple of signatures on the form to attest that there wasn't a shotgun being pointed at one of the parties' heads.
so-o many people (and there are many examples on this thread) don't actually realise religion has nothing to do with the signing of a legal marriage contract.
Something which clearly isn't true, given two thirds of marriages happen in non-religious premises. It's a miracle that two hundred thousand couples a year can figure that out, really.
because the chain of events is more or less church-wedding reception in a hotel and so on
No, it really isn't. If you phone a hotel up and ask for a wedding ceremony, they will say either "yes, we are an approved place and can organise that" or "no, we can't do that". There is no church involved in the majority - one might even say large majority - of weddings.
If you phone a hotel up and ask for a wedding reception, they will say "yes, how may we empty your wallet?" and they couldn't care less if you got married last month, are going to get married on the day or are just staging an elaborate fancy-dress party. There is no legal significance to a wedding reception, it's just an expensive way to hold a party for your friends and family.
If you wanted a wedding ceremony without a reception, they may or may not oblige. I think, I can't recall, they are obliged to offer that service of part of being an approved place, but I might be mis-remembering; certainly, they won't be happy about having the facility booked out on a summer Saturday if it stops someone who wants the full deal.
Most people who aren't desperately trying to make out that weddings are hard to organise are perfectly well able to tell the difference between a wedding and a wedding reception.
I still don't see why you couldn't just arrive in wedding clobber though??
As happens at every wedding reception, ever. No-one is in the slightest bit confused, aside it would appear from some people posting here, by the fact that a wedding reception at a hotel - even pre-1998, or whenever it was, when it became possible to marry other than in a church or a registry office - may feature someone arriving in a wedding dress. There's also nothing stopping you from booking a Saturday sales conference for your MLM in order to get a cheaper rate, and then turning up and celebrating your nuptials.