I read the project and found that people could save some money by simply transferring money or using the "transferFrom" transfer function. As such, your transactions are free. The amount of CATE you accumulate can be profitable for the transaction.
When involved in this platform, the opportunity is more for us. I like and look forward to the free CatEther product.
In practice, 0xCATE price won't be higher than the median value of a transaction. But yeah, also in practice, it should cover a significant amount of your transfer fees. In some best-case scenarios, it could even be profitable to do 0xCATE transactions in itself, filling each blocks with low-gas-price transactions.
It has two consequences: first, since Ethereum blocks can get bigger over time, depending on whether they are filled or not, 0xCATE will help in making Ethereum's throughput higher. And since there will be more transactions, it will reduce the price of transfers (since the "offer" of available tx/s will increase). As a result, more 0xCATE will be minted through transactions, which will make us enter in a feedback loop that will both make Transactions cheaper, and coin supply higher. In the end, transactions will still be free, but there will be more coins in circulation, at a same, or lower price.
When we reach the "target price" (a.k.a. transaction cost), both token price and transaction price will start to slowly decrease, at the rate of the 0xCATE emission rate. Since the number of tx/s on Earth grows at about 8%/year, if we do nothing, Ethereum gas price should increase by the same amount. However, since 0xCate has a similar inflation-%-rate, it will make everything more stable.