that is true. btc bull run affects all altcoins it hits on the scheduled plans of altcoins proving that bitcoin is thy father.maybe on trig case, there are lots of dumper before the burning of tokens held. the basic rule is the higher the demand, the higher the value and demand is based on supply the lower the supply the higher the demand thats why scarce supply of tokens will lead to higher value of AMM token
So it will be as long as bitcoin rules the world of crypto-currency. I think eventually he will lose leadership. It is not his place that the ethereum will probably rise with subsequent updates, or some other functional token. Until then, yes, bitcoin will affect all other coins.
And about burning, you all rightly said. If the burning of coins causes a deficit, then an increase in demand causes a further rise in price. I think that it will be with AMM tokens.
the demand for a coin will be regardless of whether the coins are burned or not. The main thing is that the project develop! Then the price of the coin will grow.