Not starting APU because of battery discharge is silly because in normal electrics batteries get charged. However it's true that ECAM doesn't ask you to start APU. But according to Airbus for any failure after ECAM actions are complete time permitting you should refere to FCOM for additional information. If you refer to FCOM abnormal procedures ENG 1(2) SHUTDOWN there are three notes at the bottom. The first one says:
If available, the APU may be started and the APU GEN used.
So this is the place Airbus wants yo to start APU. However because one may forget to do so, airlines have their favourite spots to start APU. Most common is at secondary failures ELEC page. However in case of APU FIRE automatic shutdown is not available in the air. So some airlines at ELEC page just push APU MASTER but not the start swich. So when you remove the status page APU page appears on SD which serves as a reminder to start APU and they start it here.