I think the problem it's from Axie Mechanism, People who joining Axie was keep decreasing everytime and it's will creating an inflation as you said
Did you imply increasing? Because the increasing of gamers will cause inflation. The decreasing of gamers will give less inflation, but not deflation. Deflation only appears if the Axie Infinity do something.
so beside doing some burning scheme or increasing the breed the fee Axie team must also creating an new game mechanism that cost SLP same like breeding, It's normal though that on every game there will be point where their native currency will be oversupply so it will be needed some update or anything like that.
Creating new use cases for SLP and restrict the release rate of SLP in the future are good. It will be supported if the team do burn events for SLP.
We see how price of BNB and ETH rose when those projects have burn events.