If your intentions were to apply:

- Mouse + Keyboard

- Screen Touch

- Gamepad Controller

Is your game limited by the least controllable/refined platform, or is there a way around such a dilemma?

Unless you're me, then you do exactly the reverse (in my case mostly because originally one of the control schemes was going to be supported). How Sol works:

Keyboard and joystick: what Sol was designed against. Four directional buttons and one jump button. Pretty straightforward.

One-switch: the first scheme I tacked on after the fact =P Hard to come up with a way to control a platformer with a single button. Ended up coming with the tap/hold paradigm (tap = quick press, hold = keep it down for longer). Tap the button to change your direction (right, stop, left, stop), hold the button to jump. It's not great and takes a while to get accustomed, but it works reasonably well. You can adjust the tap/hold threshold as well as slow down the game anyway.

Mouse-only: last one implemented, actually meant as a wraparound for eye tracking devices (so it was designed to avoid the need for clicking as well). It splits the screen into a 3×3 grid (divisions are adjustable, by default the center portion is rather small though). Moving the cursor to the left and right sides makes you move, moving it to the bottom makes you crouch, moving it to the top makes you jump. Turns out that it's pretty usable even for twitch actions (!?).

Also I never implemented touch support (since I don't care about phones and PC touch screens are gigantic), but if I had to:

Touch screen: split the screen into a 2×3 grid. The top row consists of jump, look up, jump. The bottom row consists of left, crouch, right. I haven't tested this, but assuming a decent enough touch screen (pretty much most modern phones and also some older high-end ones), this should give enough reaction time for twitch action.

EDIT: though as an addenum, yeah it probably helps that Sol's control scheme is rather simple (needing only to take care of five actions). So consider how simple you can make the controls before that becomes a problem, and then work on that to decide how each control scheme would work.