i almost bought a trailblazer some years back - right around 2001 i think. while i was debating the deal, the dealer called me back because they had taken in a couple year old 400 scrambler 4x4, which i ended up buying for about the same price as the trailblazer. that was also a 2-stroke, and i used it with the factory oil injection pump and never had an issue.
i would guess that if the injection system is not connected, then it is more likely a pump issue and not just a tank issue. assuming this is not some sort of performance modified machine, if it still works, i'd opt for the injection pump setup for ease of use. we've been using oil injection for 20+ years in snowmobiles with no issues, even on very old sleds. there's no reason to distrust it on an atv.
i find that it's often safer having things that run on straight gas, especially when they were intended to in the first place. if you had friends/family around, it's often likely that it could get filled with straight gas because that's what it is intended to run on. many people might not even consider having to use premix in today's age. that said, there's no reason that it's not perfectly reasonable to use it with premix. just a preference.