Here is a good article about how tether is supposed to work: https://bitcoinmagazine.com/articles/clearing-misconceptions-how-tether-should-and-does-work/
It sounds reasonable, but some things jump out:
BFX is the sole customer of Tether Treasure, and the single entry point for Tether issuance and redemption.
1 USD deposited can be pulled out as 1 USDT, and 1 USDT transferred in is automatically redeemed for 1 USD of BFX. This process appears to be designed for transparency, but it also serves to obscure anything that may be going on behind covers. Although the article states that Tether cannot be used for trading, the stated equivalence of USDT and USD combined with automatic conversion and the observed BFX premium makes it highly likely that all trading is in fact performed on tethered pairs. Since BFX apparently always redeems 1 USDT for exactly 1 USD, they likely treat both as equal behind covers.
Now let's take it from there:
Noble bank that served as the supposed treasury is no longer in the equation, and all signs seem to indicate that USDT is not fully backed.
Exchanges such as Binance are sitting on large USDT reserves (750 mil?), yet CZ seems unworried. Why would this be the case?
This is going to be complete speculation, but I find it unlikely that CZ spent $750 mil on USDT, or that any other exchanges actually "purchased" Tethers. Instead, my money goes on BFX acting as a USDT lender whereby they lend USDT to exchanges and receive interest payments in return (USD, BTC etc). It is probably pretty clear that this model does not work if Tether is fully backed, as lending out 750 mil USDT would require increasing deposits by $750 mil which seems improbable. Instead, Tether was likely printed out of thin air, lent out, and BFX switched to an operating model whereby USDT->USD parity is maintained by virtue of redeemability (1 USDT coming in is treated as 1 USD) rather than full backing. This scenario seems to check all the boxes:
1-to-1 backing appears to not be there
BFX EOM sales to shore up internal balances
Other exchanges sitting on massive amounts of USDT without being seemingly worried (not their money, they only need to cover loan payments)
BFX focusing on their operational liquidity in order to maintain the inbound redeemability (although all signs point to the fact that no such redeemability exists and it is instead USDT that is being used as the base, not USD).
Assuming for a moment that BFX is not a complete Ponzi, the described scenario in itself would constitute very creative and highly dangerous financing. Even without proper 1-to-1 usdt/usd backing, the operation could continue as long as BFX is able to redeem inbound Tethers for exactly $1. Tether crash would mean an instant insolvency for the firm since in that scenario Tethers could be purchased for fractions of a cent on the open market and sold to BFX for 1$. However, since Tether does come with a fancy non-redeemability clause, and BFX and Tether are two separate entities, it is likely that BFX would pull the plug on Tether before it ever came down to this. Thus, any normal business motivations that BFX might otherwise have to maintain 1/1 peg really do not exist.
Bitcoin or crypto crash would likewise lead to the same outcome as in that instance sourcing USD on demand (via crypto sales) to support inbound Tether redeemability may become difficult if not impossible. Keeping BTC price high (but not too high) would thus be advantageous to BFX.
So where does that leave us? Hard to tell because there is so much smoke. We are either dealing with a Ponzi, or with a throwback-2008-style overleveraged Wall Street firm. Not sure which one is better, but one thing that both have in common is that when they implode they do so spectacularly.
Back to your original question - could BFX somehow profit from Tether FUD? Not in any conceivable way if they are running a legitimate (or even 2008-style) operation. The only scenario that comes to mind would be that in which bulk of their assets are BTC, and they were a Ponzi. In that instance, it might be advantageous to force traders to sell into BTC in order to temporarily spike the price, offload as much as possible into fiat, and then skip town. However, that scenario seems like a bit of a stretch as the liquidity to pull off a such move is both limited and would crash BTC price thus diminishing potential future yield. So overall I would say that no, it is not in their best interest to spread USDT FUD.