Everything changes...
No. The 'finger off trigger' has NOT been taught forever. The concept began - or began being popularized - when Jeff Cooper issued his 'Four Safety Rules' in the early 1970s as I recall.
Prior to that, 'serious' holsters, for military and police use, had exposed trigger guards and triggers. As James mentions, being 'ready to fire' was taught in many law enforcement departments and agencies. Worthies such as Julian S. Hatcher, Fairbairne and Sykes, Bill Jordan and so on either taught fingers at triggers specifically or at least assumed the practice.
In the early '70s, Jeff Cooper 'edited' (I suppose the most accurate word) various issuances of 'safety rules'. Earlier versions included items like "Carry only one type of ammunition in the field; the correct size for your firearm" and "Listen and obey all range commands". Cooper was the arranger of the Four Rules commonly in use now. (For entertainment and historical instruction, do an internet search for "10 rules of firearms safety". Not all include the finger and trigger thing.)
I remember very well starting the pull on a double action revolver prior to being on target. When done properly, it is amazingly fast. Nor can I remember firing a wild shot while so doing. (I do painfully remember some wild shots shooting in other circumstances.)
Then the world changed to single action pistols. Attempting to pull such a trigger prior to getting on target is - difficult. I'm pretty sure Cooper came up with the 'finger off trigger unless' rule after witnessing and possibly suffering through some embarrassing and emotionally painful (at least) 'premature discharges' during his directorship of the Big Bear Leatherslap and other early 'combat' matches.
Not to forget, at this time in the U. S. more people were entering the Armed Forces or law enforcement WITHOUT any prior firearms experience. So agencies decided to protect the unfamiliar with technology. (Covered holsters.)
The holster makers - possibly with pressure from various agencies - started offering holsters with covered trigger guards - middle '70s to early '80s. (When I joined the Border Patrol in 1978, everyone used exposed trigger guard holsters and revolvers. When I joined U. S. Customs in 1988, we were issued revolvers and holsters with covered trigger guards.)
Safety! Most agencies are very close mouthed about ADs in training or actual duty. Not only is it embarrassing, but a history of ADs can be expensive in a civil suit regarding an accidental shot fired. However, from what I can gather talking with firearms training officers and just seeing what goes on, exposed holsters tend to have ADs on the draw stroke. Covered holsters have a few shots on the draw stroke (less than uncovered) but many more when re-holstering. Putting the sidearm away becomes more hazardous.
What does all this mean?
I gather the self-control and basic training of the individual is more important than style of holster. I have seen people - in pistol matches - who fell when running and didn't fire a shot.
Is keeping the finger off the trigger a good idea? Probably in general; but I think one should not be so oriented they cannot alter the technique when needed. It is no doubt more important for beginners.