Series vs parallel solenoids

Something I’m sort of struggling to figure out. Let’s say I have a given length of wire to make solenoids. I wrap it tightly in all cases and get some turns per distance $n$ that will remain constant, as will the current through my coils, $i$, and the area of my coils, $A$. In one case I wrap all my turns serially, like a normal solenoid. In the other, I segment my turns into multiple parallel solenoids. Intuitively, I’d expect that both should produce the same overall magnetic flux. But since magnetic flux of a solenoid is
$$
Phi=mu n i A
$$
it almost seems like my extra coils on my long solenoid are wasted. That is, I add more coils but get no more increase in magnetic flux since my coils per distance is constant. In fact, it doesn’t seem like I really get anything extra by adding more coils. But when I take those extra coils and put them into separate solenoids, since they have the same turns per length (just differing by number of turns, but that isn’t in the equation) as the long solenoid they have the same flux and superposition says if I add their individual fluxes, my total magnetic flux increases by the number of parallel solenoids I add.

So, why are these different? Why shouldn’t my single solenoid be the same as my multiple small ones? If this is true, shouldn’t physical solenoids be made just by wrapping a few turns rather than many since that’s equivalent? The only thing I can think of is that I’m using the wrong equation. That is, that equation is the equation for an infinite solenoid and I should be using the one for a finite one. But it seems like even if I have say one very long solenoid and two smaller (but still suitably long) solenoids, I still have the same problem.