I think it's not a good idea to project your own thoughts as truth, if Bittrex would see Bitshares as a competitor and would delist them for this, they would have done the same to NXT, Wave etc too. I don't know what the explanation for removal was, but there still seems to be plenty of volume within Bitshares + on Binance.
Bitshares is a potential competitor for Bittrex to a higher extent than NXT or Waves. Delisting either NXT or Waves would oblige Bittrex to remove the co-platform markets (Ardor, Ignis, Incent, Mercury and maybe some other token). There have been indeed delisted some Waves tokens - e.g. Darcrus. I am not aware of any Bitshares assets to have ever traded on Bittrex.
I am not falling for the conspiracy theory that Bittrex and Poloniex are removing their competitors' tokens from trading, rather I'd think of technical issues with the wallets (say a wallet works unstably or there are too many customer complaints about that asset vs the trading volume - I would vouch for delisting that market as well).
If the conspiracy theory were true, Poloniex never had admitted ZRX for listing.