There was a near-run on Tether this May, though, and ironically that's what pumped Bitcoin from $5300 to $8000. When folks want to dump Tether, they generally cannot dump it directly into dollars. They have to dump to Bitcoin, move it off-exchange, and then sell the dollars on an exchange with fiat currency. That means that every Tether dump creates a run on Bitcoin, which pushes the price higher. If the arbitrage trade is interrupted (as it was in May, when Binance and Bitfinex both shut down withdrawals just as the run was beginning), then the price of Bitcoin remains permanently high, and instead of selling Bitcoin on other exchanges to compensate, people buy them to match the new price, the public forgets about the panic when withdrawals open 2 weeks later, and the price remains permanently high.
I wonder also if at some point Bitfinex can just make up Tether's reserve shortfall out of their profits. (Actually, they claim that they made up the shortfall already with their Tokinex IEO, which was also super sketchy, but even if they hadn't...) Coinbase reportedly made $1B in profit in 2017 and about $400-500M in 2018; Bitfinex is of similar size, so a couple years like that and their profits could probably plug the hole, if they don't get sued/regulated out of existence first.