When starting the meeting as the alternative host, you are only taking the host controls in the meeting, but the meeting is still using the original host's license. You are just the alternative, not the new host.
If you want to get around this, try using scheduling privilege instead of Alt-host. This allows the meeting to be rescheduled for a different user, officially making them the host, not the alt-host.
Hope that helps and please make sure to mark the solution as accepted if this information is what you needed.