Taking this sort of system approach works pretty poorly in e4 openings. It works well with d4, Nf3, Nc3, g3, c4... it even works well with obscure moves like 1. c3, which is actually surprisingly decent and some people do play 1. c3. But not really with e4. In e4 openings the lines are sharp and forcing, tactical rather than positional, and not very transpositional... it's better to just consider the position in a holistic way over deliberately trying to arrange the pieces in a way where they're sort of on similar squares in one opening vs another, but all the lines will never transpose and the tactics / forcing continuations are radically different in a couple moves anyway.
There might be a little value in doing this within an e4 opening if you plan on trying out a different 1st move later on - for example, the closed sicilian / paulsen french / mainline caro-kann / vienna game all feature Nc3, and if you wanted to play 1. Nc3 later you could do that and leverage your e4 knowledge. Likewise the mainline sicilians / nimzowitsch defense can be reached from the reti. If you're selecting a line against the pirc, modern, or french you might want to consider where you're placing the bishop - the Byrne / French burn both feature Bg5 and can be reached from various d4 setups like the chigorin or trompowsky. These are cross-cutting transpositions, but beyond this... having some within-e4 transpositional opening isn't very good since it just won't transpose probably ever and e4 is not a positional repertoire anyway.
If you were to take the system approach with another 1st move it's a whole different story.
When picking a move you should consider a variety of factors...
a) how common it is, the less common the better
b) how rich it is - the more opportunities to reach novel positions the better
c) how sharp / punishing it is of the opponent vs. your own mistakes
d) how complex or ambiguous it is - I generally think the more complex / ambiguous the better since you can figure it out during preparation
e) how much theory you'll have to learn
f) what its winrates are.
g) what the engine eval is
h) how it transposes with other positions you play
i) whether it is structurally similar to other positions you play (yes it's a factor but just one of many)
j) whether you think the ideas make sense - you should have a concept of what you're doing
k) whether you find the position entertaining to play. I don't play the rossolimo not because it's bad but because I don't enjoy it
l) whether you will actually be capable of remembering it, and how intuitive it will be to play if you do forget the lines.
m) the alternatives to the move
n) other?
So you wouldn't want to ignore all these considerations just to focus on one particular consideration, especially if you're playing e4 and your moves aren't going to transpose anyway, and will all lead to vastly different positions by move 8.
People always speak about how to choose your first move, but they never speak about how to choose your second move, third move, fourth move, etc. Okay, I decided what first move I wanted to play, but now how do I decide what second, third, fourth, etc, moves I want to play? Do I just pick the #1 most popular move every time? But then my repertoire would have no coherence, it would look completely random, it would be very hard to memorize and remember everything.
As Black against 1.e4, I play 1...e5. Then, I try to play all the following moves: ...Nc6, ...Nf6, ...Bc5 or else ...Bb4, ...d6, ...O-O. This is like a "system" approach, except that it's not exactly a system because I can't just play all the moves on auto-pilot without looking at what my opponent is doing, I have to choose the move-order very carefully, I have to constantly watch out for tactical combinations (such as ...Bc5, Nf3xe5, ...Nc6xe5, d4, forking my Bishop and Knight), and often I can't play my "system" and so I have to know exactly what to do. I often intentionally choose to not play the objectively best move (for example, against the King's Gambit I play 2...Bc5 rather than 2...exf4), but White never has an advantage that is bigger than his usual first move advantage (+0.30). I am pragmatic. I prefer to transpose into my "system" rather than get a slight advantage, but I prefer to get a large advantage rather than transpose into my "system". I prefer to play slow positional variations. I try to avoid sharp tactical aggressive variations. I still don't know what to play against the Scotch and the Ruy Lopez though. Against the Scotch, 4...Bc5 has the advantage of looking more similar to my "system", 4...Nf6 has the advantage that 20% of the time it transposes to the Scotch Four Knights. Against the Ruy Lopez, 4...Bc5 (the Classical) is objectively bad, 5...Bc5 (the Classical Deferred) is no better. My options are: 5...Bc5 (the Moeller), 5...b5 6.Ba4 Bc5 (the Neo-Arkhangelsk), 5...b5 6.Ba4 Bb7 (the Archangelsk), 5...b5 6.Ba4 Be7 (the Closed/Mainline).