One issue is that it's hard to quantify the effectiveness of non-standard actions, because they rely upon (a) the player having a sufficient grasp of the imaginary situation to picture the existence of the option, (b) the DM agreeing that such an option is something the character is able to attempt, within the bounds of their available actions, and (c) the DM not deciding that it's going to require the use of a skill or ability with which the character has no aptitude.
I think this is a really major set of points here. We can unpack them a little bit, to see a bit more...
(a) The player having a sufficient grasp of the imaginary situation.
Has the GM given sufficient description of that situation?
Does the player have any narrative control such that they can make a situation happen if the GM has given a blank slate?
(b) the DM agreeing that such an option is something the character is able to attempt
Does the system work on "Yes, and..." principles?
(c) The DM not deciding that it is going to require something with which the character has no aptitude
See previous not about narrative control.
How precise are skill definitions in the system?
What kind of resources does the player have to spend to cover gaps?
D&D kind of flops on all of these. Games that allow players more narrative control, and/or have resources players can spend in a fairly broad manner will do better at this.
In Fate, a character can almost always find a way to at least create an advantage for someone - and this is the normal mode for addressing Big Bad Threats - rather than plink away with a bunch of small independent efforts that might hit or miss, like in D&D, you cooperate to create a great many advantages, and stack them up on one cinematic successful blow. Cortex+ has some similar mechanics for handing reliable and useful bennies to other players. Moves in Apocalypse World games have very broad definitions - so long as you can make a description within the bounds, an action has a chance.
Swords of the Serpentine has points a character can spend to assist cinematic actions in a way the player can expect will have impact, when in D&D, the player would have no expectation of success - I played in a game where the party was fighting a naga-like creature. It was devastating us. I would up in a situation where I looped a rope around its neck, and jumped out a window while holding the rope - there's no clear rule for this sort of nonsense in D&D.
There are things you can do with D&D to move it in this direction - allow characters to add proficiency bonus based on the action being within their general class shtick, or within their background, to cover when the character doesn't have skill - or just give everybody more skills! Allow characters to build up more than one Inspiration at a time, and spend them when they need them to try something risky.
