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 Wd1s 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.
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