Burn limits the number of tokens on circulation as well the final number of supply. A burn by limiting the tradable tokens should be able to increase the demand of the token making it's price expensive. But if the release of tokens are larger than the burn amount, it would keep on increasing the circulating coins hence the burn would have no effect.
Burn of Shiba Inu should yield a positive boost on price, if not at the moment, eventually it would have a positive effect.
I realize that it is going to be important to burn some part of the supply to decrease the supply so even if there is same level of demand then lower supply would make the price go up. However, it doesn't work for a lot of people considering the fact that we are facing situations where demand is so low that supply could be much lower and it still doesn't change anything.
I understand that it will not be at a point where it is reaching to a new level, but as long as we could end up being a bit different, it should be fine. Just get some hype, get some people very happy regarding the burn, that should be how it is and that should be how it could improve. Unfortunately not a lot of people are happy about it currently, not for many tokens at least, they just ignore it and price doesn't change much.