Yes, If

One of the main rules in improv theater is to respond to anything with a "Yes, and..." Running a tabletop RPG game is a lot like doing improv theater, so a good GM should react to almost anything the players want to do by saying "Yes, If you pass enough skill or tool checks."

This approach drives most of the action and plot in my games. I combine role-playing and rolling by adjusting the DC of the roll based on the story they tell, and how well it connects to the existing situation and facts of the setting. If they are trying to convince an NPC, I do a bit of role-playing and then have them roll for the final outcome, based on their approach.

Obviously, you should not allow players to make checks to that duplicate the abilities of a feat or another class. These rules are set and well-defined for very good reasons. You cannot let the desire for character options and agency in the moment reduce the overall definition and uniqueness of the characters, or trivialize the choices made in character creation. The rule to follow is that everything is either a character creation choice or a "Yes, If" situation. Let people make checks to do things if and only if it is not covered in the character creation or combat rules.

Aside from that, failure is never guaranteed, unless they are trying to do something very narrow or specific that breaks the rules of physics or the setting. Dice rolling is for accomplishing a goal in a complicated and chaotic environment, not a performance in a controlled athletic contest. (If there is a controlled contest, it is best to have the person with the highest score automatically win, only rolling if they are tied.) A character is not going to run a 4-minute mile or bench-press a thousand pounds just because they rolled a 20.

Success is also never guaranteed, even for things that may seem trivial. No plan ever survives contact with reality, and unexpected obstacles can always pop up. Dice rolls represent facts about the environment, and a natural 1 is always an opportunity for a plot twist that makes the story more interesting.

Combat Stunts and Pushing Your Luck

I do bend the combat rules a little, to encourage and reward skill-based combat stunts. The most common use of his is to allow people to roll checks to slightly boost their combat speed. It feels wrong and unrealistic to have a few feet make the difference between doing nothing in combat and getting their full attack action, and I don't want to run a nitpicky wargame. So if a character's speed is 30 feet, and an enemy is 35 feet away, I will allow them to move to it and attack if they succeed in a DC 10 Athletics check (The full houserule is DC 5 + 5 for each additional foot of movement they attempt). The flavor is that they are moving a bit faster than is safe, and failure means that they fall prone or suffer some other misfortune.

Hit Dice

Many things cannot be accomplished in a single action. Some might take months or years of dedicated effort. For this, you need some rules structure to force people to make choices about how where they want the plot to go, and how they want to manage their time and resources. They should be able to accomplish great and world-changing things, but only if they are consistent and dedicated and make it a real focus on their storytelling.

Also, although a role playing game is a lot like improv theater, it is also a game. There should be elements of strategic thinking and resource management, even in a game session that has little or no combat and is devoted to roleplaying. 

Hit Dice serve both of these functions, while also being a way to encourage equal participation and keep one person from dominating the session. I have written before about hit dice activities. The core concept is that in order to undertake a project, a character should spend a hit die. They then roll a skill check to see how the project turned out. If a player wants to do something grand and setting-changing that would take a lot of work, you say, "Yes, If you succeed at 25 hit-dice skill checks." When doing this, they should only get a long rest every two or three sessions, so this should represent consistent effort over at least half a dozen game sessions.