SQL Server AutoClose option
15K databases on one instance of sql server - depending on the activity, overhead of maintenance, backup time, etc sounds to be an overkill.

You should instead spin up VMs on one powerful host machine and then balance out your databases on multiple VMs.

You are looking at a wrong place for optimization - Auto-Close option and you know that what you are trying to do is not a good practice either !



Remember: Auto-close is deprecated, so one more reason to avoid it.

Seems like you should invest in reading - Multi-Tenant Data Architecture