There is a lot of "STUFF" out there and some of it isn't fit for human consumption.
Yes, there are some riders who've had mechanical issues to contend with and if there is a company that has never made an engineering faux pas... well, to paraphrase a famous text, "let those who are truly without fault cast the first stone."
"----------- caused by being air cooled / ---------- caused by being a pushrod engine" The number of people who think that an engine is doomed to serious mechanical issues just because it's air cooled or has a push rod operated valve train is scary. Push rods are often used in place of over-head cams because they are RELIABLE and they allow an engine design that's not so tall. Many modern engines use overhead cams. They also typically have shorter strokes and spin to high RPMs. Want BIG power? Build an engine with four valves (or more) per cylinder, add as many cylinders as can be fit into the chassis, make the bore about twice the stroke (or more), make compression something that scares the hell out of the connecting rods and pistons and make it liquid cooled. If that's what you need, you probably should own a Ducati. The Thunderstroke, by design, is a slow spinning, under-stressed, long stroke, low RPM / moderate HP BIG TWIN. It IS what most of us have asked for for decades.
Think push rods are a problem? Usually it's a matter of push rods or OHC... then BMW came out with cam-in-head design. See, overhead cams make the heads very "tall". Often a lot taller than the cylinders below them. So BMW put the cams in the sides of the cylinder heads. They're chain driven and have very short push rods operating the valves at the "top" of the heads.
How about the modern large displacement air cooled, push rod Yamahas? The Yamaha Road Star, Roadliner, Stratoliner, Stryker 1600 through 1900cc models have two push rods per cylinder, one push rod tube per cylinder, and four valves per cylinder. Their history has not been without issue, but none of the issues are related to air cooling or valve operation.
From an engineering perspective, I can find little fault with Polaris/Indian's choice of engine cooling or valve operation. It IS a HEAVY engine and I think that they could have pared weight down considerably if they'd have tried at all. It passes modern pollution standards without needing a radiator or the additional weight, plumbing and complexity that goes with it. Still, do try to avoid stop-and-go traffic in hot weather. Using push rods allows for an engine that's both prettier and not so tall. Witness the Victory big twins. THAT is a TALL engine.
For a long stroke 1800cc narrow-angle big twin, Indian made a compact design. Staying away from overhead cams, having no frame tubes below the engine and running the upper frame close to the rocker covers keeps the center of gravity low, making low speed maneuverability easy and the overall heft feeling much lighter than would be expected of the actual weight. From the rider's seat, I think that Indian hit a Grand Slam.
From a mechanic's point of view... DAMN! You can't pull the heads off without having to first remove the engine entirely from the frame. With special tooling you can swap the cams and you can service the clutch, but not much else without having to pull the entire engine. Grrrrrr...