I think under very ideal control conditions it is possible to launch an aircraft fully loaded with a ski ramp HOWEVER for all intent and purposes you can't ( I think that's what popeye was refering to).
With a catapult you can launch anytime anywhere w/o so many restrictions.. with ski ramp you can't unless you have that perfect weather, wind speed etc but even then you SHOULDN'T.
You are risking unecessary safety as well. Besides the last thing you want going through a naval aviator's head is him sweatin bullets as he's about to launch because he knows his bird is carrying tons more ordnance than recommended for launch. He may overcorrect, make mistakes or just poop in his pants
I believe the kuznetsov was designed from the outset to be able to launch fighters with near full payloads under most circumstances reliably. but a catapult mitigates for various dangers, include a sudden engine failure during takeoff, and a lack of headwind hindering a large payload takeoff. Also catapults allow for AEWC to also be launched of course.
Do we seriously think India would have purchased vikramditya if they could only launch their mig-29Ks at a fraction of their payload (considering that A, India is on a shopping spree for the best money can buy, and B, the mig-29K isn't exactly a large aircraft to begin with so any decrement in payload and fuel load will make it almost tactically irrelevant)? Even the latest concept for a new Russian carrier carrying PAK FA is a SKI JUMP concept.
Ask around on any of the Russian aviation boards (I think they would know more bout their own nations aircraft than we do), you'll get a similar answer for the question of kuznetsov.
Yes we don't have any pictures of kuznetsov launching fully loaded fighters. That isn't because it isn't able to. Rather it is because the kuznetsov was launched as the USSR was dissolving and the russian navy since then could barely keep their ship oiled up and fighters maintained, let alone arm them enough to take off with large loads. As liaoning and vikramditya enter service, I expect you guys will finally get the pictures and videos you want of J-15 and Mig-29K taking off with large payloads. Until then, please think critically about what evidence we have that says fighters cannot take off from ski jumps with large payloads, outside of repeated dogma from western military "observers" that have never taken a moment to even calculate whether their conclusion was feasible.
Catapults are still better than ski jumps. No question. Cats can launch large fixed wing AEWC, and larger subsonic high aspect ratio aircraft. But both can launch decently loaded fighters. Under what conditions, and with how much reliability accounting for variance of engine reliability, is another matter. But trying to dichotomise catapults and ski jumps based on fighters and their payload is flawed and reductionist in.