Apparently, these commemorative coins did not sell well in 1923, and some were dumped into circulation at face value. I have had the good fortune of having looked through the collections of two California-based gentlemen who appear to have mainly collected from circulation. Each of these collections contained one of these Los Angeles-Monroe Doctrine Centennial Halves in XF condition, much like yours.
The Monroe halves are notorious for weak details, even on uncirculated specimens. I bought one in a 2nd-tier TPG holder graded MS-63 that had less detail than Johnny54321's coin. If this coin has significant remaining luster I'd say it's probably at least an AU-50.
They are very interesting coins with a significant historical theme. This one looks above-average for detail. Nice!
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