Monthly or weekly token burn strategy is no longer an alternative solution to increase token price, as you said it is better to add burn 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.
Even then this is not completely alternative way but without this option currently it is very difficult for alt-coins to survive if the supply continues to increase. As was the case with Luna we know. There's lots of token whos price is decreasing continuosly Due to not having this option. So my opinion is burning is one of the most important thing to increasing price. Just as the central bank of a country controls inflation by controlling the printing of currency, the price of tokens can be controlled through burning.