Splinterlands is a good example here but I believe that it's quite exceptional to see such a growth in members. On the other hand there are mechanismes in place that increase supply when prices go up and reduce supply when prices go down. Tokens like DEC are far from being minted at a random pace. There are also mechanismes in place that actually burn DEC and SPS I believe (sales of DICE packs, tournament fees).
I think that burning, if kept dynamic can be a good mechanisme to actually react to demand increases or decreases. In my opinion, a tribe should work on both sides of the scale. It should work on increasing demand and also do something to reduce supply.
Yup, DEC has both dynamic inflation and burning, but as you can see they are both ineffective mechanisms during exploding growth. When demand really soars inflation can go high without any consequences, except good ones, because it allows smoother and quicker growth. In Splinterlands case, I believe the higher inflation 'doesn't work' because there were no packs to buy and the cards on the secondary market are limited compared to the growth level.
The same is true if there isn't enough liquidity and a slow mechanism to release more liquidity (Hive), while expecting serious growth. That's why I don't believe in the burns of Hive.
Not a good combination is if a token has a high liquidity, high inflation and slow or inexistent growth. Then burning is a way to prevent the token depreciation, until ways to stimulate growth are found.
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You sum it up very well. I think it is also important how much a token is distributed. If you look at hive, it is distributed among thousands of accounts which is positive. Some tribe tokens are spread much thinner. The smaller the distribution and the more inflation, the more it makes sense to burn some tokens I believe. The best is to do the same than Splinterlands.. Exponential growth. In this case burning is definitely not necessary lol