It is all about the ratio between Bitcoin paid for security and the total value of transactions in a block.
Something like security = (fees+mining reward)/(total value in a block).
You are right that the price of Bitcoin increases and as such even a small mining reward is a lot of payment for security, but the value of the transactions in a block also increases proportionally.
It becomes very obvious if you start calculating in Bitcoin instead of calculating in fiat value.
The current block reward is 6.25 BTC/block since the last halving 11th of May 2020, meaning that at that time the cost for securing a block was halved, but the value of all Bitcoins transacted in a block did roughly stay the same after 11th of May 2020.
This means that the transaction costs have to go up to secure the transactions in a block. Especially at times there are few transactions, this means that security might be outright to low to secure a high end transaction. Hence, a supply model like grin is much more secure on the long run. Other alternatives exist such as spreading the transaction feest over multiple blocks. But in all cases spending is not stimulated since transaction costs will be high. What is needed is a balance, meaning not to much supply to avoid inflation, not to low supply that security is weakened. Grin aims to strike that balance and stay future proof. This quote from Tromp explains it perfectly: