The value of the USDT is not a real value, meaning that there will be no printing of that money. Rather, it is just a tool used to stabilize prices at a certain point. Therefore, I believe that this value will work against crazy rises and will not affect the value increase.
Generally, aren't platforms supposed to burn some USDT?
That's actually not the case. Tether is backed by fiat (USD/EUR)... or at least that's what they claim.
As for the burning, that's done by Bitfinex since they are the ones who own the token.