"Extra flourish isn't how I would call it."
Yay, great fantastic... Thats whay dictionaries are for... Finding other words to describe all that jazz after the "and".
As for frighten via intimidate, you can frighten someone thru intimidation but not necessarily Frighten then. The conditions are prepackaged sets of calculable programmed effects.
Intimidation is not, to me, that precise.
Maybe the target runs, maybe they move to get a weapon, even if that is closer. Maybe they move to attack you to keep you away from their babies. Maybe you become the focus of their fire. Maybe they close 15' to cut the rope you are climbing across on.
Some of those things are strictly illegal if you are allowed to inflict a pre-packaged condition that strictly forbids them closing with you even if its the only way to eliminate you as a threat.
Thats the difference between a magical compulsory control and an emotional reaction to an intimidating or even down right scary person.
Skills generalky, create the wide world of expected unpredictables... While magic typically is handled differently. There are some overlaps... Being knocked prone still produces the same condition - whether ots by a magic push or a shove. But then if the magic persists and holds you down, thing get different.
But, as always, a gm in their game can rule it how they want.
If in your games, beaches enable bonus action blind attacks or mountain crushing flourishes or whatever, thats between you and your players.
Be At Peace, always.
The way I see it, it is a big and fundamental approach to gaming. THE big turnover for me in 3.X / 4thE era was the "Hard Rules" approach to gaming: you couldn't attempt anything if you don't have a specific rule that grants you such thing. That is, if you want to throw sand in the eyes of an enemy, you need a feature that grants you such attack as an encounter power, or is nearly useless/ you just can't. It is a very video-gamey approach (no judgement involved, i LIKE videogames), in the way that you need a specific piece of code to attempt something. I'm more a "Soft Rules" player: specific powers do a thing better than average, but you can
still do them as its most basic level, with skill checks. That is how it worked (somewhat) in AD&D, and later in the OSR movement: you can always try something, and it is up to the
5th Edition takes this approach to its heart; even the
stunned condition is depicted as an ogre hit by what appears to be a halfling with a hammer. Most spells or special abilities grant bonuses in addition to the "average" result, take for example the Battlemaster maneuvers: they are common attacks with increased damage (superiority dice)
and an effect, such as Frighten, knock an enemy or Disarm it. The same happens with the Open Handed monk.
There are some of these conditions with their own rules (like Disarm, in the DMG), but they are left to the DM to asign the actions and effects. The PHB advises to use skills creatively. If the game should need a rule for every minor interaction, the game will suffer of an extreme rules' bloat. That's why I, as a DM, take the approach of cost-opportunity for improvisations, applying common sense wherever it needs to have a limit. Even the game says so in the PHB. 5th Ed is a fantastic
system, because it can resolve many things without too much effort, always following the guidelines, and not a collection of seemingly unrelated rules (a la AD&D, which was my game of preference before 5th ED, but it
was clunky). You always have the Skill Check, Attack and Saving Throw mechanics to resolve things. Specific beats general, and it is often better than a simple skill check (EG, the Shield Master feat allows to perform a shove as a bonus action, instead of spending an attack).