Just for clarification, Dash is not a private coin.
Monero, Zcash : privacy-centric cryptocurrencies (meaning privacy is key focus for these cryptocurrencies and privacy is also their only use case. These cryptocurrencies have closed blockchains)
Dash : transaction-focussed cryptocurrency with optional privacy (optional privacy, which by the way is used less then 1% on Dash network. Also Dash has an open blockchain, just like Bitcoin)
Dash optional privacy is based on Bitcoin's CoinJoin, only implemented on a core level and expanded with more rounds to mix. There is currently more mixing occurring on the Bitcoin network
then on the Dash network .
Link :
https://bitcoinmagazine.com/articles/percentage-coinjoin-bitcoin-transactions-triples-over-past-yearThis leads me to conclude that Dash is less likely to get delisted, then privacy-centric cryptocurrencies with closed blockchains (where senders / receivers / amount can not be traced)
If an exchange delist Dash, that exchange may as well delist Bitcoin (which Dash has been forked from). Most exchanges view Dash the same as Bitcoin with regards to privacy and from a
legal/compliance point of view.