I do not think the premise is correct. Following Brüderland and Volker in Best & Wolf The SAGE Handbook of Regression Analysis and Causal Inference [square brackets have my remarks]:
Both estimators require strict exogeneity [Fixed Effects (FE) and First Differences (FD)]. However, while FE builds on
the assumption of no serial correlation prior to demeaning (see condition (15.10)), FD relies
on no serial correlation in the differenced errors. The latter assumption is equivalent to very
strong correlation in the untransformed errors. FE and FD therefore rely on assumptions that
are opposite extremes.
So both estimators require strong exogeneity.
This being said FE has and serious advantages over FD. Again following Brüderland and Volker:
Any of the four basic within estimators is appropriate for dealing with time-constant confounders. Nevertheless, FE regression has some important practical advantages over the others. ...
FD might be preferable in the presence of strong serial correlation.
However, besides that advantage, it has the disadvantage of being inefficient because the initial
period is dropped in any case. Moreover, the inefficiency can be very large in the presence of
missing data, because first differences can be built only on ensuing observations. For example,
if one person is observed at $t = 1, 3, 5,$ then FE would use the three person-years, but in FD the
person would be dropped completely. With (balanced) panel data for $T = 2$, the DiD estimator
is identical to FE and FD. For longer panels, however, it differs in general. In fact, it can give misleading answers because all variables enter the regression in levels. If there are control variables (which usually is the case) their effect is likely to be biased, which may also induce bias
on the treatment effect. It is therefore recommended to use FE (or FD) where all variables are
transformed (Wooldridge, 2010, p. 321).
The advantage of FE in terms of not wasting precious observations should not be underestimated. While things are getting better and nowadays you will often be able to have access to panel time series (panel data with very long $T$), in past as well as still in present to a non-trivial extent, most panels have very short $T$, in such situations the last thing you want to do is to waste extra observations, and FD has also other issues as mentioned above.
This being said if the level data exhibit very strong correlation you would probably get better results with FD so FD is not useless, but often FE is better more suitable.