"In this day and age, they all should be scanned and posted on a probate office website."
No.
Until the Will goes through Probate there are a lot of reasons why it may never get that far!
Will is improperly executed. Will was made under duress. Testator did not have capacity.
Which is why you are correct when you say: "Probated Wills are public records accessable to all"
"To be honest, if the contents of Wills were publically 'read' in advance of probate then it would eliminate a lot of bad feeling, confusion and possibly even underhand behaviour in a lot of cases. "
As it happens, I agree. But, in my experience, there is nothing like the sniff of money to turn people into nasty, grubby, underhand etc.,etc. In most situations, there will be harmony and agreement about what should and will happen. In the cases I've seen, where there is disharmony, you can trace it back to the dynamics of family living and the desire of (e.g.) the Testator to cause as much grief in death as he did in life!
mf