ok lets think about your "suggestion" here.
how much bitcoin are we holding? 1? 10? 100? or 1000?
how many people will burn bitcoin? is it only 10 person or is it 10,000
and also the most important question that you need to answer is that will you be really willing to throw away 10% of your money away just for a "chance" of maybe causing price to go up just you threw away some money?!
the answer is clearly no. nobody is going to throw away thousands of dollars just for a crazy chance.
and besides why don't you start thinking about how you can increase the demand instead of reducing the supply?