TL;DR:
In order to add flavor and significance to the player's choice of character class, ability modifier, and skill proficiencies, skill checks should be automatically passed if:
[(character level) + (ability modifier) + (proficiency bonus)] > [2 x (skill check difficulty)].
This would allow highly proficient characters to bypass rolling the d20 for certain skill checks entirely, which would streamline gameplay, avoid frustrating critical failures, and add further significance to the character choices the player makes at the beginning of the game.
I would like to suggest a change as to how low-medium skill checks can be passed.
Right now, characters with high ability modifiers and skill proficiency do receive some benefit in terms of passing skill checks, but even low level skill checks are largely dependent on the d20 roll. Ex/ even a character that is highly intelligent (18 INT, for a +4 modifier) and proficient in an intelligence governed skill (+4 proficiency bonus) can still fail fairly low skill checks (difficulty level 10 or lower), if they are unlucky enough to roll a nat 1.
This, in my opinion, weakens the significance of a character having a high ability score and being proficient in skills. It reduces key character decisions, such as class, skill proficiency, and some racial traits, to a nothing more than a statistical advantage over a blank Tav.
I believe that giving characters a way of auto-succeeding skill checks will help to establish meaningful flavor and specialization on a character to character basis, and allow crucial character decisions to play a more significant roll in out of combat gameplay.
I propose that if the sum of the player's character level and total skill modifier is greater than or equal to twice the difficulty of the skill check, then that character should automatically pass the skill check, no roll required.
Equation:
If [(character level) + (ability modifier) + (proficiency bonus)] > [2 x (skill check difficulty)], character auto succeeds check.
Example:
Level 12 Wizard with 18 INT and Arcana proficiency
12 (character level) + 4 (INT modifier) + 4 (Arcana proficiency bonus) = 20, so this character will be able to automatically succeed Arcana checks of difficulty 10 or lower (20/2 = 10).
Allowing these low to medium skill checks to be auto succeeded and bypassed, if a character is proficient enough, will add gravity to character decisions made at the beginning of the game by streamlining low-medium skill checks (no roll required), while at the same time preserving the current difficulty and equation for higher level skill checks. It would also avoid the frustration of having to burn inspiration on a re-roll when a supremely intelligent and proficient wizard fails a test of basic magic knowledge via an unlucky nat 1 roll, or similar situations for other classes.
This change would make the player feel as though their character choices matter more in out-of-combat gameplay, without disrupting the game game balance of the higher difficulty level skill checks.