I've never fished jigs/t-rigs on it. Nor would I ever try to. It doesn't have the backbone that you need in my opinion. I mean, I guess you could use any rod you want, but you'd need to really swing hard with the moderate to set a stout hook.
I do, however, fish pretty much any moving bait that fits into the weight specs of the rod.
I don't think you'll find any 1 rod that is great for every bait. You can probably break it down to 2 though. 1 rod for moving baits (MH Mod) and one rod for jigs/t-rigs/frogs (MH F or H F). If I'm pong hopping and looking to only bring 2 set-ups, I bring my 7ft Abu Vengeance with Black Max for moving baits, and my Berkley Lightning Rod with an Abu Silver Max for my jigs/t-rigs and frogs.
I'm sure people will disagree with what I've said about these rods. But I'm a budget fisherman. I'm not going to spend a ton of money on a rod. These 2 setups probably cost me a total of $140-$150 and I've been fishing with them for years now. Are they the best quality? No. Are they the lightest rods out there? No. But you'll be able to cover pretty much all of your basic techniques with these 2 rods.