How do you make a platformer with no jumping?
That’s easy: momentum
If you can’t physically jump to get over a gap, you need to build up speed in accordance with the level and launch yourself across the gap. You can bounce off walls, you can run off ramps, and if all else fails, gravity is your best method for gaining speed.
I find this approach way more interesting and fun than just “you need to press A to jump over the gap”.