It really depends on what a person does whether amateur, hobbyist or professional.
With only the three planes mentioned how do you cut slots for box bottoms?
Attachment 443136
Or rabbets?
Attachment 443137
It is convenient to have a shoulder plane to clean up a rough rabbet:
Attachment 443138
Having a plane to round over a sharp shoulder is also an improvement on leaving things rough:
Attachment 443139
Before all of this was done the pieces were trued with a #6 and smoothed with a #3 & #4.
It is true one can do basic joining, flattening and smoothing with a three plane set up. Especially if one is working the same projects repeatedly. If one is always making different sizes of different objects it is easier to work with tools sized for the job.
A realistic way to determine what planes one should acquire is to first determine which plane is the best suited for what one wants it to do.
jtk