What you're referring to is 'broad comedy' - and that's my point. They don't make them in a big way.
The films listed above are not 'broad comedies' they're comedy/dramas.
I'm not sure of the 'Mel Brooks is not an argument' (link in one of the responses) is a defence at all, because the fact is, he took excessive risks while trying to make a point, risks which would not be made today.
He was Jewish and took on very serious issues with Nazis ... but he definitely was not Black, and Blazing Saddles ... wold be too much for today.
By all accounts, Tropic Thunder would not get made today because of the ostensibly 'blackface' character - I think that's a really good 'threshold' to analyze because while I don't think the character is generally offensive and most wouldn't see it as that - but it's definitely going to be for some, to the point where Execs just couldn't back making the movie. There's going to be guaranteed outrage, and that outrage, if the press decides to amplify it, will kill a film and have all the parties involved running scared with apologies.
The Kids in the Hall (Kevin McDonald) indicated they couldn't make what they made today. They did indicate they got pushback back in the day from some of their bits that mocked religion - particularly from the US - but they still got to make it, which is the point.
Casting for any role which involves 'mixed' anything is a minefield which risks overthrowing a project. The casting of Cleopatra (who was Macedonian), caused controversy by people speaking on behalf of ... Ancient Egyptians? Whom even modern Egyptians could hardly make a claim to?
There's a lot of good talk about having more people from different backgrounds in roles, and especially have them among rank and file production, which is obviously good, but this should be a different theme from say, what jokes are acceptable and not.
Those are different kinds of issues that are getting crossed up in a cacophony of Twitter noise.
HBO, Disney and Netflix are not interested in creative expression, they're inserted in products, broader audiences, and films that speak to their choice narratives. If you listen to some podcasts you can hear the opinions of these executives themselves speak about it. These are not your 'creativity first' type of people.
Cable TV has always allowed for a narrow set of channels that challenged conventions, kind of a 'Late Night Loophole' in which naughty stuff was tolerated. We need this equivalent for streaming sources. We need an 'Adult Swim' version of Netflix that invests heavily in outrageous things.