So far monthly burns give imho no impact. Like the price was 3 cents during good times, it stays the same all the time. Bitcoin price change is the only thing that impacts on the price. I dont even think that burns really helped. I might even consider not doing burns, but keep more mineable tokens. Imho, adding more usability to token, or perks for holder (more you hold, better bonus you get) will be a better solution. And by perks I mean not distributing more staking rewards, something else.
Monthly or weekly token burn strategy is no longer an alternative solution to increase token price, as you said it is better to add burnt allocation for holders profit than burning it without price increase effect, it can also be added for new utility for holder and create big reward to attract investment from new traders.