Hi,
I do not work with the Automic team so I cannot specifically comment on your incident, but in general, I can tell you that we have customers using it to contact us on the UIM team frequently, so I know it does appear and customers are using it! It is true that when all engineers are busy or otherwise engaged, the Chat feature may not be available.
Regarding the second bit - some clarification is warranted. The chat function will put you in contact directly with a support engineer, not a development/product engineer; so you will indeed be using a "quicker avenue" to contact the usual support department engineers, not a shortcut to bypass them and speak directly to development.
For this reason, the Chat function is probably more appropriate for simple/quick questions -- "The documentation isn't clear, can you tell me if X version of your software supports Y version of the Operating System?" for example, or "can you tell me if there is an option to disable the software from doing _________?" whereas if you have an issue that requires engagement and troubleshooting, it's very likely that this will be converted to a standard support case anyway. On a severity-1 "production down" situation your best bet is to call the Support Center directly for the quickest response.