I understand reasons not to make gear swap between champions free. This is a different approach.

When a champion is equipped with a gear piece, it goes to that champion's inventory.

When a gear piece is removed, silver is not charged and an item stays assigned to that champion.

When another champion is equipped with that piece of gear, it moves to another champion's inventory, and silver cost is charged.

Gear assignment still feels permanent. 

Free gearing for every arena fight is still impossible.

The problem of having a small set of gear that every team uses is still impossible.

It may lead to even higher silver consumption than current approach, because players will assign more gear to champions. Players may be tricked by "free" gear swaps, that are not actually free in the long run (I know Plarium doesn't shy from such tricks :) )

It solves Doom Tower problem of having to equip a champion with a particular gear set for a single fight and then removing it. Players can assign two gear sets then.

It also makes possible implementing of gear setup saves that can be equipped with a single button provided that all pieces are in one champion's inventory.