To the best of my knowledge, No. Transaction fees are not part of the security design of Monero. As demand increases, so does block size. (This solution was rejected by bitcoin several years ago and is the "blocksize wars").
This means more of the transaction confirmations can be processed for each block, in BTC this is a hard limited, leading to increases in fees.
It's like there only being one Bank for a city and everyone must only use one bank branch, the cost for getting to and into the branch to deposit or withdraw money would be very high, people would pay higher fees to people closer in line, to cut in.
In XMR fees might temporarily increase in response to a spike, but will trend back down. Like building a bank branch that can increase or decrease in size at will to house with so many tellers, no one has to wait in line.
That there is a small fee at all is to provide some small positive incentive to miners/nodes for running and to reduce abuse, spam.
When Btc fees increase, the economic principals at play by design, are the assumption that more miners will come online to meet demand and return to equilibrium(lowest fees possible). As new miners come online, we will see the fees go down again, in BTC. This has happened many times, with a backlog in low fee ordinal tx's being cleared recently.
Monero has taken a unique activist, grass roots based security/hashing architecture. Mining and fees are both non economic, this places Monero as private cash.
You might also be interested to look into how tail emmisions in Monero make it different then BTC.