I can think of two good reasons to model diminishing returns with the natural log.

Logs produce nice units in the regression coefficients. A log-lin function (that is -- log'd dependent, linear independent) says that a percent increase in X results in a <coefficient> unit increase in Y. Similar statements are true for lin-log and log-log, the latter of which produces elasticities.

y=ln(x) and y=sqrt(x) will both fit data in a similar manner, so it makes sense to go with the one that makes for easy interpretation.

Additionally, the natural log frequently shows up in financial economics, most prominently in continuous interest but also notably in returns, which seem to follow the log-normal distribution.