Discussion: Does sharding have an effect on ETH demand?

I’m trying to better understand the underlying drivers of ETH demand. To me there are three main factors:

1. ETH as a store of value
   The more people/institutions view ETH as a good store of value, the more they will buy/hold ETH, which obviously drives demand
2. ETH being directly used in DeFi
   The more people/institutions choose to use ETH in DeFi applications, the more ETH will be bought, held or locked in smart contracts. For instance, if someone wants to take out a loan in ETH, then the party providing the loan first needs to buy/hold the corresponding amount of ETH, which increases demand.
3. ETH being used to pay for gas
   The more people use Ethereum, the more they need to buy ETH to pay for gas. Since the network has a certain gas limit, gas is a scarce resource. The higher the demand for gas, the higher the gas fees become. This means when the network is used more, people need to buy more ETH to pay the gas for their transactions, which increases demand.

So far so good. Now, what I find a bit difficult to understand is point 3 after the implementation of sharding:

Let’s assume sharding was successfully implemented and Ethereum’s computation power increased by ~64x (assuming 64 shard chains are used). This means that the gas limit of the entire network is ~64x higher than before. If the demand for gas (measured in ETH) stayed the same, this would mean that the gas price would decrease to 1/64 of today’s value.

So overall, the amount of ETH paid for gas and hence the demand for ETH is not directly affected by scaling Ethereum via sharding. The demand for ETH would only indirectly be affected, because when the gas price decreases, it makes certain new applications economical that weren’t before. These new applications would then add to the existing gas/ETH demand.

My questions:

• Does my reasoning make sense? Or do I commit a fallacy somewhere?
• What about the scaling via rollups, does this have an effect on the ETH demand?

Any opinions are greatly appreciated!

TL;DR
Three main factors drive demand for ETH: Use of ETH as store of value, in DeFi applications and for gas payments. Sharding does not change the ETH demand directly. Do you agree?