It's totally possible to play at a high level without tap jump.
Most people who play Project M competitively are coming from a Melee competitive background so tap jump is just something they are already used to. Playing without tap jump just requires the same getting used to that playing with tap jump required for Melee.
Some things like Up B and Usmash OOS are impossible to do using the standard input without tap jump so you have to find some other way that works for you to do them. An Up B or Usmash OOS is actually a jump canceled version of its respective move. You can't directly Up B or Usmash out of shield, but you can jump out of shield, and you can cancel a jump directly into an Up B or Usmash. With tap jump on, you just have to input the Up B or Usmash as normal, and it will automatically jump cancel it for you. Without tap jump, you have to manually jump cancel them, which involves inputting a jump and the attack at the same time; something along the lines of hitting X and B/ X and A while holding up on the analog at the same time. My friend only uses R to shield/l-cancel, so he remapped L to jump. When he wants to Up B or Usmash OOS he hits L and the attack input at the same time, which he finds easier than hitting X or Y and the attack input at the same time.
Just an example, it's really all about personal preference and what is easier/more comfortable for you.