My point being look at who is buying Tether and you'll see it's actually keeping money out of the market, aka inflation sponge. That is my point in this line of questions.

BTW, while Tether has created a USDT token on top of some blockchains such as Ethereum and Tron, they have not, and cannot, create their token on the Bitcoin blockchain. This is actually an objective, technical limitation of that blockchain, not some sort of subjective policy.

What specific mechanism would cause the price to go lower?

What a loaded question. Go back to basic principals: Price is always based on supply and demand. Let's talk about Ethereum first, and ignore how you can buy USDT directly through exchanges. People who want to interact with USDT token on Ethereum blockchain need to obtain ETH to submit transactions. If they are not miners (who can mint new ETH), and are not selling goods/services for payment in ETH, then they need to buy it from someone who will sell it. This creates demand, raising the price of ETH. If Tether abandoned Ethereum, there'd be less demand for ETH and the price would go down.

But what impact is there on Bitcoin? You can't trade USDT on it, so demand/supply is not directly correlated. The speculative value people put into crypto trading would certainly go down if all stablecoins disappeared, and that would cause Bitcoin's price to fall too. But USDT isn't the only stablecoin around (USDC is the main competitor), and speculative trading directly between tokens (no stablecoin involved) is still very popular. So the overall impact on demand wouldn't drop as much as you might think.