Take-off would not be an issue with springboard, but can you explain how do you consider TVC would help there?
Have you ever been in a small motor boat?
When you are just sitting in the water and turn on the outboard motor the boat goes from sitting deep in the water to rising up and riding on less water... this reduces the drag the water imposes on the boat so the boat can go much faster once it is up and out of the water.
By changing the angle of the thrust from the outboard motor you can help the boat sit up out of the water allowing it to go much faster than it would if the thrust was fixed and designed to hold the boat down in the water.
By changing the trim of the engine propeller wash you can rapidly lift the boat out of the water so it is almost plaining... this is not a hydrofoil but uses a similar principle.
Now think of an aeroplane taking off... the first thing you do when taking off is angle the nose of the aircraft up 15-25 degrees or so to increase the wing angle and generate more lift, but with fixed engines that means the engine nozzles are now pointing down when in actual fact you want them pointed horizontally backwards to generate the most forward speed you can manage to accelerate faster.
On a Harrier jump jet in a rolling takeoff the engines are not horizontal and they are not vertical either, they have them at 45 degrees backwards to generate lift, but to also generate forward speed so the wings generate lift as well to support the aircrafts weight and to allow it to get airborne with more weight.
With a modern fighter whose engines don't go down 45 degrees... and even if they did you wouldn't use that setting because the engines are at the back and the rear would flip up and the nose would go down because it is not balanced lift you would never do that... you would either vector the thrust down to assist with lift generated by the wings or angle the engines up to angle the nose of the aircraft up to maximise acceleration while using maximum wing and fuselage lift.
TVC is also very useful in very high speed flight because the engine nozzles can be used to trim the aircraft instead of control surfaces... using tail or wing surfaces to trim the aircraft in supersonic flight increases drag and also RCS with deflected tail and wing surfaces... using the engine nozzles improves high speed cruise performance.
In any case, the thorny issue is the landing as far as I can see.
Arrester hook landing is the best option for all aircraft... TVC and large wing area means lower landing speeds which is always good, but catching cables is the best way to land.
Stop saying stupid things likr that. You need something that works always not in specific conditions. What if you send 10 su-57 in the air for training and the ship's stop working ? You loose 10 su-57, almost 1 billion dollars.
You have inflight refuelling aircraft that can allow them to divert to friendly airfields... besides when landing they will have very low fuel and they never carry a heavy weapon load... their primary function is air to air so most of the time when they land with full air to air weapons they are much lighter than when they took off.
Why would the ship stop working?
One of the offshoots of the EMALS work... they could incorporate the landing system with the cat launch system so that as well as accelerating the aircraft for take off it could also slow down aircraft for landing using an EM system.
And by the way if the landing system did fail pointing the ship into the wind and accelerating to max speed is the first thing you do before trying to recover aircraft... it is just common sense.
With the expression " without special means" are they implying that it could possibly perform a shipborne rolling landing i.e. without the need of arrestor cables?
There is a land based cable landing system that uses trucks with the reduction gear and cables spread across an highway that can be used to land aircraft in shorter spaces of tarmac than what they could normally operate from... but I suspect they just mean "without assistance".... ie no cables, no brake chute...