  The cluster Westerlund~1 (Wd1) is host to a large variety of post
main-sequence (MS) massive stars. The simultaneous presence of these stars can
only be explained by stellar models if the cluster has a finely-tuned age of
4-5Myr, with several published studies independently claiming ages within this
range. At this age, stellar models predict that the cool supergiants (CSGs)
should have luminosities of $\log(L/L_\odot) \approx 5.5$, close to the
empirical luminosity limit. Here, we test that prediction using archival data
and new photometry from SOFIA to estimate bolometric luminosities for the CSGs.
We find that these stars are on average 0.4dex too faint to be 5Myr old,
regardless of which stellar evolution model is used, and instead are indicative
of a much older age of $10.4^{+1.3}_{-1.2}$Myr. We argue that neither
systematic uncertainties in the extinction law nor stellar variability can
explain this discrepancy. In reviewing various independent age estimates of Wd1
in the literature, we firstly show that those based on stellar diversity are
unreliable. Secondly, we re-analyse Wd1's pre-MS stars employing the Damineli
extinction law, finding an age of $7.2^{+1.1}_{-2.3}$Myr; older than that of
previous studies, but which is vulnerable to systematic errors that could push
the age close to 10Myr. However, there remains significant tension between the
CSG age and that inferred from the eclipsing binary W13. We conclude that
stellar evolution models cannot explain Wd1 under the single age paradigm.
Instead, we propose that the stars in the Wd1 region formed over a period of
several Myr.
