I have seen many exchanges have launched their own token like Binance with BNB, Idex with IDEX, Hotbit with HTB, Yobit with YO etc. where exchanges use their own tokens as another way to pay fees to support token. In addition to it, different strategies are used to create a hype like decrease in supply etc.
But if an exchange goes through a hard period of time and shuts downs then ultimately that token will come to its end because there is no community other than that exchange supporting the token simply because it has no usage outside the exchange.
According to me exchanges should promote the usage of their coins/tokens outside the exchange to build a community in support of it. If your community consists of huge individual entities who believe you then a great community can be formed. Otherwise lack of applications would lead these things to disaster.
Actually you made valid points, but I was just thinking what an exchange token utility will be outside the exchange, that means they will have a huge competition to face because there are tokens already trying to pitch their tents in various sectors and industries. Also, about an exchange shutting down, that is quite true as well because many exchanges has shut down due to hack and so on but however since till date no exchange token has been used outside the exchange (none I can remember), then it makes sense to only hold top exchanges token because they have their reputation to protect and will surely try everything possible to keep their exchange running, thus good for holders as well, and should there be a change in token utility then holders will also benefit from it.