Hello! League sound designer here chiming in to add to this discussion. Like you pointed out above, it would add a lot of unnecessary noise into the game that is already hectic and filled with lots of auto attacks, skill shots and voice lines firing off.
Gameplay clarity is key - we only add footsteps to Spells that convey movement (Nunu's W, Mordekaiser's W, Warwick's W, Teemo's W... wait, why are all Footstep sounds on W?) or sometimes as flavor in Homeguard animations as champions are seen running out of the Base.
Sometimes, in rare cases, Kled has footsteps because it's part of his gameplay to know if he's on Skaarl or not.