“Bitcoin is a store of value because it stores value across time.”
Is that something you heard & repeated or just made up? In either case, read it back to yourself a few times and see if it makes sense to you.
Your definition as something that must "have value beyond that which is given it by its proponents", which is an idea unique to your imagination.
A store of value is essentially an asset, commodity, or currency that can be saved, retrieved, and exchanged in the future without deteriorating in value. In other words, to enter this category, the item acquired should, over time, either be worth the same or more.
Understanding a Store Of Value
Feel free to explain how this doesn't apply to Bitcoin.