"I watched Columbo when I was growing up." You're giving away your age, @Caroline03 :) -which is why I'm not going to discuss why Kojak was the cooler detective.

@Ultraviolet Ha Ha! Gosh - how funny clean humour is! When we allow ourselves to laugh at each other in good-natured FRIENDSHIP! Yet, that is something that we evidently must NEVER do today!
I think that the reason these films don't get aired anymore is that somewhere within them you find clear evidence of a Christian culture that modern day society seeks to represent as pagan earth-worship and the Vatican clearly is the figurehead for it all!
Another Film was done around the same time as "The Great Race" called "Those Magnificent Men in their flying Machines." I'll link it below at a significant place. During the film, a group of Nuns help the Italian get back in the race, just so the " Protestant " won't beat him! That's it! Unheard of in a modern day secular production, clear representations of normal people including Jesus in their films in some way or another! The Herald of the new dawn, replaces good old fashioned humour with "woke" Christianity. Instead of pious references to Faith these days the innocent family films are banned, whilst those adering to our Faith are called bigots for daring to mention His Name at all!
It's funny - because people ARE funny! They are flawed, ego-centric and vain - even though they admire Christ. In the section of film I've time-linked below. I've edited the best bit by far of the film Ha Ha! The Italian Pilot in the race depicted the archetypal normal Italian Roman Catholic of the old era- He even had a large family and sings like Pavorotti! He crash lands in the grounds of a Convent, and asks the Sisters to hold down the tail of his plane so he can take off again and get back in the race. The Mother Superior, as she might well do, tells him to remove himself and his flying machine at once, proclaiming stiffly "We have no interest in worldly matters" With a flash of inspiration the Italian Pilot plays an Ace, "Mother, if you don't help me get back in the race the Protestant will win" Simultaneously the British Pilot's plane flies overhead to put her in the picture. Then, the Nuns hitherto crisp none-colloquial accent vanishes and hollering at her sisters in a broad Irish brogue she urges "Sisters don't just stand around gawping - this good Catholic needs our help"
Classic! Even though I was a Protestant myself as a child, I roared with laughter and will do now!! Even though I wasn't of the faith, I knew what Catholics represented. Yet, I knew (no doubt from a film education such as this) that Catholics were proud of being extremely faithfully Catholic and supported their Church ! It remains amusing, because that Mother Superior reflected the pre-Vatican II Lay Catholic's mindset - initially, apathetic to the Italian's need for help regaining the time he has lost in the race she gives him full support when she realises that a Catholic may lose the race to a Protestant because of herself! So, in her mind, they are like minded working towards the GENUINE common good - Faithfulness to the Church! - if people don't laugh at it, perhaps they don't respect or value Our Lord's true Church highly enough themselves?
Why aren't we able to view such healthy films on TV any longer? Why? Because the noble Roman Catholic Italian Pilot, was the archetypal old time Catholic, who had a large family and nowadays, the RC Italian, no longer HAS 6 or 7 children, and the modern audience has been adjusted to view Christians as being other types of people who are pro-choice and contracept etc... Trad. authentic Catholics smile when they see his portrayal of a Italian with 7 children, who sings Sacred Arias in his plane like Pavorotti, and is hoping to beat the Protestant in the Race. However,- in today's culture,nobody would laugh with approval, they would jeer, deride and mock! As in the same film today, his modern day equivalent would not really care whether the Pilot likely to pip him to the post is a Catholic or not!
So much has the Church of the past been corrupted. To be really "Catholic " in 2021, in the eyes of the world, you have to judge the two characters in that sketch as bigotted and racist! Ouch!
As for Ireland? That sweet Nun would now be reprimanded by her Bishop and vilified for being unecumenical.
ok.ru/video/634008242762
Likewise, the last film of the trio filmed around the same time that I admired as a child was "Monte Carlo or Bust" (In America it was called "Those daring young men in their jaunty jalopies." ) I never liked Peter Cook or Dudey Moore much, yet, they did a good job of playing two British Army officers back on leave from the Punjab! HOW politically incorrect it is! A bit like Python has become!
You couldn't even say the Hallowed Name of "Christ" within a non religious film today - yet in true British style, and a reminder of our society when we were growing up before this modern anti-Christ era, Peter Cook for all his pomposity,in the film bears witness to GOD on many occasions! Pompous twit! I haven't watched none-religious films for years. I turned off the modern films upon my conversion - yet how everything has changed! Nowhere in today's secular comedies is there any reference to God. Due to that, How shocking even this simple impious reference to Christ is in Monte Carlo or bust (I'll link below for this one too)
Peter Cook "I think it's pretty obvious who's side the Lord is on Barrington"
Dudley Moore "England's Sir?"
Cook "Naturally!"

ok.ru/video/2425189829300
I doubt if either of these films would be shown on TV today. They depict an era where Christ was still very much referred to within cinema - borne witness to by normal everyday folk often vaguely, but nonetheless He's there somewhere! They deny His influence spans 2000 years and how it was HIS influence that founded Western Civilisation ALONE! Communists and other evil people HATE to acknowledge that fact and I believe that it is the reason for our new anti-Christian culture banning all mention of Christ from within film. It's not that we think Peter Cook is JUST that we snigger! Any more than people laughed when Python ridiculed (in advance) the Gay Soldiers on Parade. Conservatives laugh ! Liberals HATE that! We laugh at our failings and they don't! That is the honest truth!We don't think Peter Cook's Racial bigotry is just, if we DID - let's face it, we would not laugh at all! We are in a world where none of us flawed sinners are permitted to make references to God and that is shocking!

@Caroline03 Many "old movies" depict a better and long-gone era, even in purely secular terms. Alfred Hitchcock's horror/ suspense movies are shocking experiences when the viewer focuses on the -society- of that era... clean streets, well-dressed people. It wasn't just "Hollywood" either.
Vintage photos from that era support Hitchcock's depiction.