Sure we do. Everyone who is present to hear the officiant say this was also present when the legal requirements were met, and was a witness to their being met. So they know they were met.
Plus, the laws of most jurisdictions don’t require the officiant to say this. Saying it is just a tradition. It has no legal significance.
I’m glad it wasn’t the indoor shed. 
They haven’t moved the goal posts: they’ve just changed the signage. Ohio has child-support guidelines that no longer require “marriage” to prove “liability”.
Child-support doesn’t directly relate to marriage. Establishing liability for child support is not really relevant to whether a couple is married, even if marriage has traditionally been used to establish liability. There are no children mentioned in the OP.
In the U.S.A. and some other Western countries you’re either married or you’re not.
Not so in Thailand, where there are four distinct “ways to marry” which (with one exception) can be combined in any combination:
[ul][li] live together as man and wife[/li][li] register marriage with the District government[/li][li] perform the wrist-tieing ritual[/li][li] have a wedding ceremony (making merit to an odd number of monks, etc.)[/li][/ul]
The exception is that a wedding ceremony will always include the wrist-tieing ritual. A young couple living together who intend to have a wedding, but must wait to raise a satisfactory bride-price are faced with a dilemma. A wrist-tieing would effectively deny the intention to have a wedding, but failure to tie wrists would annoy the ancient animist spirits and signify that the couple is living in sin.
Yes. What I said. You’re still liable for child support, even though Ohio no longer calls it “marriage”.
Child support doesn’t have anything to do with marriage, common law or otherwise.
Unless you are legally married in some states but not others. SSM used to be like that along with a couple of other states where marrying underage girls is legal (Kansas comes to mind).
Each state is still a society.
You are tempting me to get into a battle of pedantry. Tempting, I say!