This is what happens. Loopcuts will not wrap the object around but are placed only on two of the four faces.
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A loop cut is defined as an edge loop, i.e. a chain of connected edges which separates two neighboring quad loops. It works best in a topology of quads, and your mesh is a lot more complicated. I suggest you separate the 'fingers' of your topology by adding edges, and take it from there.
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$\begingroup$ Although I know what you try explain, it has to be a face with four edges (often called quad) for the loop cut to work, not a vertex connected to exactly four edges. If that was the case, you couldn't cut a simple plane for example (two edges per vertex), or a cylinder (three edges per vertex)... the loop cut also works on quads even if their vertices might be connected to five or more edges... $\endgroup$ Commented Jan 17, 2022 at 22:15
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$\begingroup$ I stand corrected. I have yet to see a correct definition of edge loop in blender, so I gave it another go. $\endgroup$– eezacqueCommented Jan 18, 2022 at 10:48
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$\begingroup$ Well, it's not working "best in a topology of quads", it's working only in a topology of quads. It stops where there are no more quads to be cut. From the Blender manual: "The to be created edge loop stops at the poles (tris and n-gons) where the existing face loop terminates." $\endgroup$ Commented Jan 18, 2022 at 11:14