I feel a bit wary of « chat support » environments.
Same. Chat might make some sense in a company environment, like for a social backchannel or “where to go for lunch today?” But in a support or community context where most folks are participating asynchronously, IMHO you’re right to be wary: offering chat for anything serious might set an expectation of instant response. It creates more channels for helpers to monitor, and requires overhead to moderate and to convert any chats that warrant preservation as topics.
You might have a use for chat strictly as an off-topic stream of banter – or you might consider launching without chat and see if a need arises naturally. It can be easier to hold something back than to take it away later if it does become a headache.