macOS status bar: Change keyboard layout icon
Solution
If you just want to get rid of the flag, you can use the identical ABC input source instead.
If you make a copy of the US layout with Ukelele, you can add any icon you want. If you do not provide any icon, just the .keylayout file, then you should get exactly the "simpler icon" you show in your question (except the US will come after the icon).
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