The Vulcan is to me an example of how desperate the SLDF was for mechs, any mechs at that point in the Amaris War. It isn't a case that they're choosing to deploy Vulcans instead of Firestarters, it's a case where they're already deploying every single Firestarter they have, can build, and can buy/steal/savage, and STILL need more infantry-defense mechs, and that's where the Vulcan comes in. It's not the best or even very good, but it's the best at being available.
In that vein, I see this as a second-line infantry fighter versus the front-line Firestarter. The Firestarter is what you use to hunt infantry, the Vulcan is what you use to defend against infantry. Infantry tends to include small support vehicles such as pickup trucks armed with support weapons...or bombs. I could see a Vulcan being invaluable in the base defense role, using the autocannon to destroy incoming suspected car bombs before they can get to the gates. As others have mentioned, it's also useful for trying to park heavier vehicles before they get into range or hitting incoming aeros.
Regarding the -6M, I feel like this is less about trying to improve an anti-infantry mech and failing, and more about repurposing it out of that role entirely. This is a persistence hunter, meant to use its mobility to stay at its range of choice, and just pelt a single target with 8-point slugs for an extended period of time. The rest of the weapons are pretty much just close-in defenses, not part of the primary mission profile. In-universe, a commander would be best served assigning a pilot with above-average gunnery scores to this machine. Out of universe, BV you spend upgrading this mech's pilot are going to be disproportionately useful.