I understand better.
"What is visible" is really a flattenned stack of the visible layers (with an eye in the Layer dialog).

Not exactly flattened but merged
Flatten will a remove the alpha channel, replacing any transparent area with the background color

The question is the interest of this command. Alexia, please, could you detail your example?

well i can not reply for Alexia but i may give a example.

On a hypothetic image add a duplicate layer on top in Overlay mode give me excellent result to enhance details and contrast on some area But terrible result on others

On the other hand a similar process but in Multiply mode will do the opposite ,improving that part (i.e under-saturated and too pale sky and clouds)that overlay mode will screw up ,but worsening the rest,

with NEW from visible i may save, and then merge the best of both combination easily

apply new from visible for combination-1,(overlay) toggle off visibility of that new layer, repeat the process to save result of combination-2(multiply)

then i may erase with more on less opacity what i do not like on the New merged top layer and when happy of the combination , save

you will not able to get the same using "merge visible layers" once merged will become impossible to recombine the layers in a different mode,

You may not need that feature

But if you would need it , without NEW from visible,you would need to get trough 5 no too much intuitive steps instead then a single click