Nothing leaves a ski jump much faster than about 80 knots; that's the whole point of the ramp, to get you airborne before you've reached flying speed. If you were to take off from the ramp like a car or motorbike, you'd fly for a while then drop back to earth/sea once your momentum ran out. Jet Aircraft are still accelerating when they leave the ramp, and they reach fully wing-borne flying speed a few hundred feet ahead of the ship and about 200ft above sea level.
While that is all correct in principle, there will nevertheless be a significant difference in speed between a STOBAR and STOVL aircraft as they leave the ramp.
Has to be, because the STOBAR aircraft must be closer to flying speed at that point for it not to violate the same minimum altitude limits during the "semi-ballistic" part of its trajectory. Unlike the STOVL counterpart it cannot rely on a lift contribution from the engine, but that's fine since using all available thrust for acceleration (especially aided by retractable chocks) provides for correspondingly greater aerodynamic lift.
The ramp is the cheap and easy way to do it, the penalty for non-vectoring thrust aircraft like the SU-33/J-15 is decreased payload/fuel load, limiting the potential usefulness of the aircraft.
Decreased compared to a STOVL aircraft, at least the F-35B in particular? Nope.
I don't know whether it is, potentially speaking, possible to design a STOVL fighter which beats the payload range of the Su-33/J-15. For example by removing the weight penalties imposed by stealth or increasing size to Flanker-levels. However, the F-35B definitely is NOT that aircraft - as mentioned in the carrier thread, not even when taking into account a F-14-like fuel reserve in the Su-33 for bolters. Do the math using the weights given in Blitzo's original posts and pay attention to fuel fraction at comparable payloads. And that's before we get to scenarios where bring-back is the long pole in the tent - the Su-33 has no problems at all in this regard.
At the same time the point about MTOW compared to CATOBAR which the original source makes is admittedly misleading as well. Yes, STOBAR can get an aircraft comfortably in excess of 30t off the deck, but that neglects to consider what fraction of this total weight is payload and fuel. Launching an aircraft off the deck is not an exercise in breaking MTOW records, it's a means to an end: delivering explosives on a target!
Using that criterion and assuming a "Su-35-ized Su-33" (slightly higher empty weight, more fuel & big thrust hike) as an indication of the full STOBAR potential, you find it approximately equivalent to a F/A-18C or Rafale M. That's a creditable showing (although the only reason it manages to just about match Rafale is the MTOW restriction due to the 75m catapults on CdG) but falls short of the Super Hornet.
What's more, it means you need a ~19t OEW STOBAR aircraft (and correspondingly more fuel) to do the job of a ~11t CATOBAR aircraft! Effectively this at least partially negates the ship impact and cost benefits of losing the catapults too. For housing and handling an equivalent number of the bigger aircraft, a STOBAR carrier will require a larger hangar, flight deck and aviation fuel bunkerage. Essentially, you need a somewhat bigger ship!
So no, STOBAR is not a viable replacement for CATOBAR, but all indications are that it is superior in terms of mission performance to STOVL.
As impressive as it is in terms of an engineering achievement, the F-35B does strike me rather as a solution looking for a problem. Like I said, stealth with all its weight penalties due to internal weapons bays, coatings and large fuel capacity is pretty much the antithesis of STOVL requirements, so the very concept is insanely ambitious. To have pulled that off is a resounding success, how does it pay back though?
The short legs mean the carrier has to approach pretty close to the enemy coast, which seems like a big risk if the enemy's defences are indeed sophisticated enough to require a stealthy aircraft. What's the use of a survivable fighter when you have to put the ship in jeopardy to use it? Yes, yes - sortie rate ("it's not a bug, it's a feature"). But what stops you from parking a CATOBAR carrier just as close to the opponent if and when conditions allow? On a 65000 ton, 280m by 73m platform I doubt CATOBAR deck ops will come with an efficiency penalty worth mentioning, anyway.
Cost? Ok, the ship definitely gets cheaper without catapult and arresting gear, but isn't that penny-wise, pound-foolish when the airgroup becomes more expensive instead, with all the added complexity of a powered lift system? Not to mention the impossibility of providing equivalent AEW capability, no matter the money.
The only real advantages I can see are training (a short take-off or landing is much the same on a ship as it is on land) and perhaps airframe life (catapult launches and arrested recoveries are hard on the structure). If these factors are really that critical though, maybe it's time to ask yourself if you really can afford a carrier capability in the first place rather than accepting a contrived half-way house.