Yes the Avons "check". I've had a few sets that have. They stayed on the bike and I rode the hell out of em. Never had a failure, never had one so much as even whimper, wet or dry. I think the checking issue is a non-factor to be honest. Should it happen? Likely not. Is it a true safety issue? I've logged roughly 40K on various sets, never had a problem with them. Not leaking, no structural failure, nothing.
Yes they absolutely DO need to be run at higher pressures. If you run Road Riders or their venom X counterpart (only available in the front size anymore but the combo IMHO is better than the Roadriders on both front and rear, the venom bites a little harder which gives that "on rails" feel in long fast sweepers) at the factory suggested pressures they will not last. They'll check worse, they'll saw tooth, and they'll flat out the center. I'm not light by most measuring sticks; 6'4 down now to 245lbs but was up to 280 at one point!! And I ran one up at 38 front 40 rear. Two up or with luggage add two pounds each end.
They are pointy as Brian said, which removes the slow tractor like feeling from the comparatively long wheel-base GS models (KZs had a bit shorter wheelbase, and while that made them feel more nimble, they could be a bit scary at speed and headshake was an issue when rolling on throttle out of the apex...this issue is still a Kawasaki trademark as evidenced by my ZRX) At speed however, the Avons pointy profile does not take away from the GSes nature to generally be rock stable at high speed runs. I've tested this thoroughly

Pointy, aggressive steering tires (or I guess tyres since we are talking Avons here) can sometimes lead to skittish behavior in long corners, the bike not wanting to stay on the desired line...never have had such a problem out of these.
I've never tried the sport demons, as I felt I would go through way too many tires a season, and the added "sticky-ness" didn't outweigh the added hit to the wallet, as the Avons had never let me down in fair comparison at high lean. (Though, chuck sand or gravel under any tire and they're likely to squirm a bit

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But I have tried BT45s. Didn't like em. Tried a couple of Cheng-Shin. Didn't like em. Dunlops, nope. I always came back to the Avons. My last GS I didn't keep long enough (either time I bought it...heh) to go through the Kenda Challengers it had on it. Those were the single scariest tire I'd ever ridden on. In the dry when pressed not even as hard as I would normally press a tire (and there are many guys on here who would press harder than I, I'm not saying I'm Joe Racer, but I like to push it when the mood's right) they felt greasy...in the wet? They felt downright dangerous. Definitely NOT confidence inspiring at all.
I damn near low-sided a GS1000G with those fitted to it, with Rose on the back. Bless her heart, she said afterwards she knew we were in trouble when the bars were pointed the opposite way we were going. But she never grabbed me up or freaked out. She said she just hunkered down behind me and tried to stay as centered on the bike as she could. She said she knew I'd either pull it out, or we'd try out the new gear we'd just picked up over the previous winter

Man I got an awesome wife!! Hahaha! Somehow, through sheer muscle memory and instinct, I kept it up, stayed on the gas and worked the front wheel back on line, it was over before I could even process what happened. But I'll never put those tires on my bike, nor will I aid in spooning them onto anyone else's.
They might be ok for a Sunday rider who putts around, but if you ever get frisky, there are a slew of other tires out there that are tens of hundreds of times better suited for the job that cost the same money or so. Kenda Challengers are probably worse than some of the mediocre tires that our bikes could be outfitted with when they rolled out of the showroom. And I mean that sincerely.