There is nothing wrong with using dice if you like. The design of the scenario shouldn't rely on success at these rolls in order to continue. The secret doors in my home made dungeons usually lead to extra treasure or other "bonus" material. Nothing that will end the scenario or the entire campaign if it isn't found will EVER depend on making a roll.
Fudging to get a desired result is the biggest waste of time ever and antithetical to playing a game in the first place. If a secret door MUST be found or else the universe encounters a page fault simply decide that the last person using it left it partially ajar. Then say " there is an open secret door there, wanna check it out?" Beats the hell out of tossing dice over and over for a foregone conclusion.
That's fine, but it prevents some perfectly valid and fun scenarios.
I almost always refer back to what I think as the atypical D&D adventure: An ancient tomb created by a powerful wizard forgotten by time. The wizard was so greedy that even in death he wanted to make sure no one took his wealth, so he created a dungeon filled with powerful magic traps and creatures who would guard his treasure for all eternity. There is but one record left of the tomb's existence and it happens to come across the PCs path. Will the PCs go and find the ancient wizards fortune? Can they beat the traps, monsters, puzzles, and obstacles put into their way to get to the end?
Of course they do, they are the heroes of the story, and like all heroes they will be the first people to defeat the traps and get to the end because they have the skills necessary to do so, far beyond that of normal people. They are all good fighters, they are all skilled in navigating hazards like the kind they'll come upon in the dungeon.
The ancient wizard was tricky and hid the treasure beyond many secret doors and traps. Success requires finding all the secret doors and avoiding or disabling all the traps. Which they will, eventually, by persistence and skill. Because otherwise, the story is about a bunch of bumbling idiots who found their way into an ancient tomb and FAILED to get past the traps to find the treasure. That's what happens in real life, not in fantasy stories.
The last person in couldn't have left the secret door open because there has never been another person in here. There is no hidden map of the place because that would defeat the point of making an almost impossible to navigate tomb to protect your treasure. There are no people who you can ask who will give you hints as there's no one left alive who knows the inside. There's just not a good story reason to leave the door open. It makes a better story for there to be a secret door and the PCs to find it than to not have a secret door or have it mysteriously open.
Everyone CAN contribute during a fight, some just aren't very good at it. Wanna talk about heroic? Last session in my OD&D game the elf (adventuring as a magic user), stepped up to the front line to replace the hobbit fighter who took a mortal wound. He stood there in his AC 9 robes with his 4 hp and held his side of the line for 3 rounds before being cut down. All combat rolls were made openly, he just frikkin did it. He did what needed to be done although obviously unfit for it. What a hero!
That's not heroic. That's dumb luck. Marvel at the prowess of the great wizard who, though completely inept at combat, stood in front of the enemies and hoped that the DM miraculously rolled poorly enough for him to survive.
That scenario conjures images of a frail elf in robes walking up to a line of goblins and closing his eyes and holding a staff out in front of him while the goblins tripped over their own feet repeatedly just as they were about to swing.
I'd prefer heroes like Gandalf in the Lord of the Rings movies who kills a number of Orcs in a couple of seconds with his sword than the above scenario.
There's a reason that everyone in the Hobbit and Lord of the Rings eventually learns to fight. They wouldn't be decent adventurers if they didn't.