Eth has better price and is terrible to use because every transaction has a burn.
So first off, I'm not all that knowledgeable about Ethereum so I could be wrong here, but don't the gas fees go to the miners? As far as I'm aware there's no burning going on there.
In any case, burning is good for token prices...I don't think it's possible to argue with that, it's just simple supply/demand. But, asking people to burn STEEM (or any token) is just flat out never going to work. Asking business to create a product that requires burning STEEM is no different. A few people here and there might burn some to be altruistic or make some type of point, but at the end of the day it's money and people aren't going to burn their money.
To make burning work, it has to be part of the platform. This is what you're doing with Steem Engine and it's working great there (as far as I can tell at least). Steem already has this a little bit with account creation. You can burn 3 STEEM to create a new account. This is a great example of how burning can be used as part of the platform. Of course, after HF20 now you can claim free accounts using your SP so I suspect not many people are doing this anymore.
In my opinion, SMTs should work very similar to how Steem Engine works - you should have to burn STEEM to create tokens and even more to enable other features like ICOs, market trading, staking, proof of brain distribution, etc. As an example, Tron has a built-in smart contract for creating tokens that requires you to burn 1024 Tron to use.
Overall though, even if these all sorts of burn mechanics were implemented I doubt it would make any meaningful dent in the STEEM supply. If we want to focus on supply, I think the focus should be on reducing inflation and/or the Steemit, Inc selling; however, I think the real focus should be on the demand side.
If SteemIt, Inc wanted to I'm willing to bet they could make a deal with some big company like Samsung, or get STEEM listed on Coinbase, and just one such deal like that would do far more for the price than anything we might do on the supply end.