OK, how would the following relatively uncommon historical forms of execution become more widespread- at least in Western countries- before 1800 ?
Boiling alive
Breaking on the wheel
Crushing
Flaying
Impalement
Roasting alive
Breaking on the wheel and crushing were already widespread and common in most of Europe up to the French Revolution. Really the main country which didn't use them to any great degree was England, and they had their own favorite forms of painful execution...hanging, drawing and quartering, etc.
I think the problem with boiling alive is it involves the use of an apparatus which could be dangerous to the executioner. A person put into a pot of boiling water or boiling oil might struggle so much that he or she upsets the pot and spills the hot water or oil on the executioner. This is obviously undesireable and would make it difficult to find people who would take the job of executioner.
As for roasting alive (I suppose you are not counting burning at the stake as "roasting"...that's more like flame broiling than roasting), most likely the reason for that is the lack of "entertainment/education" value for the masses coming to watch the execution. Putting somebody in an oven and locking them in, you can't see them writhing in pain, and you might not be able to hear the screams.
As for flaying, not sure why that went out of style. The Assyrians used it quite a bit.
As for impalement, also not sure what would make that more popular. My guess is the reason it wasn't popular is that its quite difficult to get right. If you don't insert the stake in just the right place, you'll kill the victim right away before any of the "fun and educational" stuff starts.

So other forms which were easier to accomplish without great skill were likely favored by most.