We can design a game from theory first: start with a premise, decide on major goals, and then design systems and mechancis that will function, while meeting all the goals, and still adhering to the premise.
One trouble is drift. Goals tend to accrete, making the project more elaborate. We fall in love with certain mechanics, interactions, or side-effects of an in-process design, and so add them in to the "must have" list, constraining all further design work.
Another trouble is that our premise may not be coherent or very plausible: our goals may be in conflict, in practical ways, and possibly theoretical ones too -- which weren't obivous until we got into the guts of the design work. As goal accretion happens, it becomes less and less possible to satisfy every goal; or even if it is possible, it's less possible to do it well: every aspect of the game becomes compromised in some way.
ftenually the result of this approach is unworkable, and must be abandoned. But a messy, grab-bag game is another possible outcome. Sadly then, the hope that from clear and simple premises can flow an orderly and focused design is generally ill-founded. It really only works for very small games -- where, in reality, the mechanics were probably already in mind from the beginning.
Instead of this mush, let's envision an alternative process. It keeps concept and mechanic close: every time an idea is imagined, it is set into concrete form with a specific mechanic; with dynamics, variables, randomizers, whatever is necessary. All of these are temporary, and may be modified, so it's iportant not to sweat the details too much -- even while it's critical to have detail anyway. You will also have to guess about what else might be going on in the game, for this mechanic to mesh with -- fine, guess: just label placholders, like "links in with reward mechanic here" in your notes.
Each concept/mechanic pair is a little module. And by adding more, you can start to build up a feel for how the whole thing will look, in terms of elaborateness, major dynamics, similarities between mechanics, and numbers of interactions and variables needed. You may decide that things need to be simpler.