I ordered an Arrieta 801 N with side clips in the late 1980's.

With the gun closed you could see daylight between the sideclips & matching cut in the bbls (think large dead cat) & I could see no evidence that the sideclips came to bear when the gun was fired either. In this case the maker obviously thought sideclips were totally cosmetic.

In a gun with the lumps properly fitted to the action it's difficult to see how sideclips would improve on lateral support but they don't hurt anything & look traditional on a heavy proof gun.