Do any exchanges support Monero integrated addresses?
For those that do not yet support them, have they shared the reason why?
Poloniex is the exchange with the most Monero liquidity currently and now supports integrated addresses
Another large exchange Kraken has supported Monero integrated addresses since XMR trading started in January, 2017.
Update: As of August, 2017 there are at least two more exchanges that support integrated addresses including Tux as mentioned in this answer and xmr.to. Based on current trends the level of support for integrated addresses is likely to increase in the future.
There are not any major exchanges that support integrated addresses yet, but that is likely to change:
Shapeshift is having its development team look into supporting integrated addresses
There have been efforts to automate the generation of integrated addresses in order to make implementation easier