This I can agree with but that's not exactly what your previous statement said
That said bitcoin's payment or remittance functions are what make the store of value function valuable.
Does the payment system make BTC potentially more valuable than other comparable store of value (gold)?
Sure, but gold itself is a great example of a SOV with a very limited payment function that is still relatively successful because of its sound money functions.
If you argue that the payment system is what will make BTC mainstream, beyond the sound money property, then yes I would tend to agree.
Yes that is what I was trying to say.
BTW although gold has a very limited payment function, that payment function was the best function available at the time it was used, and it did work pretty well. With gold and silver coins someone could simultaneously carry enough to live for a year and also have small enough denominations to pay for dinner. That is pretty functional and was good enough for a time, but not as functional as dollars, and definitely not as functional as Bitcoin.