It really is a viable idea BUT
First of all, most helpdesk software apps already do that. It's just not marketed loudly and not on the surface. [shamelss plug] for example, our app has integrations with JIRA/Github/Bitbucket/etc. And also Trello/Asana whatever.
Second of all - these days, with things like IFFT, Zapier and SaaSler, when people with literally no programming experience can connect two different apps together (like Trello goes to Github, then Github goes to Basecamp, then Basecamp triggers some Invoicing app etc etc etc) - the "integration product" niche is kinda shrinking.