Tomb of Horrors has a long and storied history. It was originally developed by Gary Gygax the co-creator of D&D specifically to kill high-level PCs:
First, Gygax explains, "There were several very expert players in my campaign, and this was meant as yet another challenge to their skill—and the persistence of their theretofore-invincible characters. Specifically, I had in mind foiling Rob Kuntz's PC, Robilar, and Ernie Gygax's PC, Tenser." Second, so that he was "ready for those fans [players] who boasted of having mighty PCs able to best any challenge offered by the AD&D game."
This was an adversarial style of play: the DM was actively playing against the other players.
Modern methods of play assume that the DM is working for the players (except, possibly, during combat) with a focus on enabling them to over come the challenges but not destroying them. This was not an assumption inherent in the early days of D&D.
It was expected by everyone around the table that exploring dungeons was dangerous and that you needed to do it carefully and be ready to run from anything you weren't sure you could beat. 1st level characters bumping into an ancient blue dragon? Must be a Tuesday. Hell, we never even gave our PCs a name till they reached third level and you wouldn't pay to raise anyone less than 6th level or so.
Tomb of Horrors is not unique in this, most early modules contained "save or die" situations, however, the Tomb turned this up to 11 - in fact, its its own trope. The most important part of any PC's inventory was the 10-foot pole for poking at things from a (relatively) safe distance - of course, dungeon designers (DMs) know about 10-foot poles so they would put the trigger over there while the trap was actually right here.
Further, concepts like mechanically implementing skills like Perception or Investigation did not exist. These were not PC skills, they were player skills. If you wanted your PC to see something you damn well told the DM what you were looking at, what you were looking for and that you did it with both eyes open, right eye closed, then left eye closed then with your head on the right side, then left side etc.
Old school play involved being very specific about what you would do: "I open the door", DM says "How" and so begins the sequence - "I push the door", "I pull the door", "I slide the door left", "I slide the door right" etc. For an old school player, the sequence you describe is nothing unusual - most would breeze through each of these rooms pretty rapidly. The whole purpose of the doors was not be a challenge in themselves but to lull the players into a false sense of security that they might forget to keep checking for traps and so get give the DM their "gotcha" which is what all DMs lived for. Of course, experienced players would never be so foolish.
This is, to modern players, an alien and disturbing mindset.
As to "how to give your players a chance"?
You have the wrong mindset to be playing Tomb of Horrors - players have and deserve no chance: that's what makes it fun.
I believe Matthew Coleville's quote captures it nicely:
I think it's a mistake to think of the Tomb as anything other than what it was intended. Gary's answer to players who came up to him saying "My character is unkillable. I've already killed the Tarrasque and Tiamat and Orcus and all the gods."
It's mostly a bunch of unsolvable "fuck yous" each of which is designed to kill your character without a roll.
If you're having the problem Gary had, then it sort of makes sense. Though I suspect there's about a million better ways to deal with that. Otherwise, pass.