It is unfair to include Ronald Reagan in that bunch.
True, his 1986 legislation did include a ONE TIME offer of amnesty.
But it also beefed up border security and contained penalties for businesses that hired illegals.
It was Papa Bush who reneged on this deal and backstabbed us by loosening the controls and opening the floodgates in 1990.
Klinton and Bush II are both guilty of being intentionally derelict in their responsibilities in this matter.
Well, you're welcome to that opinion, but the amnesty was a carrot to the burros, and so he shares some of the blame (IMO).
The problem is - there were seven more amnesties afterwards and although there were penalties, they remained/remain largely unenforced. So while I see your point about Pres. Reagan, that did keep the ball rolling for extended open borders.