To answer your headline question:
A level deck allows for faster take-off with a greater payload than a ski-jump.
The ski-jump system has been used for decades, with the Royal Navy developing them in the 1970s. The Harrier "jump-jets" used in the Falklands in 1982 perfected the ski-jump launch - see this pic from Wikipedia's ski jump launch page for example:

The ski-jump is useful for reducing the take-off speed required to launch, but it has some risks for aircraft that cannot thrust vector as airspeed reduces after launch...
And that leads to other downsides, including reduced payload:
However, ski-jump launches cannot match the payloads made possible by high-speed catapult launches. While aircraft such as the F/A 18 that are normally catapult-launched can make use of a ski-ramp, this typically comes at the cost of a reduced capacity for either fuel or munitions, and thus negatively impacting mission scope significantly.
(also from that Wikipedia link)
So...why not use a catapult and a ski jump? Well, the catapult would have to stop before the ski jump, as the mechanical stresses involved in trying to have a straight then curved catapult make it impossible to maintain, so the highest speed would be at the base of the ramp. Which means the ramp then has to change the vector into an angled up course - that's a lot of strain on the undercarriage. So much so that even without a catapult, it broke various aircraft undercarriage when higher speeds were attempted.
Additionally, you don't want to expend energy to then have the speed reduce during the ramp phase - you get better bang for buck accelerating the length of the flat runway.