Would be interesting if the rules forced damage to the attacking player if they didn't use a weapon of some sort. Say... 1/2 of the damage caused? Weapons, being built to handle the stresses of attacking, would take no damage.
When I'm GMing a game in my AU, or even most general games, I tend to use a few special rules for melee weapons and physical attacks.
Kicks = Apply the movement modifier for kicks twice, and no -2 bonus. It makes no sense that a giant robot running top speed is more likely to be able to stop and kick an opponent than punch them, or even hit them with a laser. As such, a stationary mech is even money TH, but a walking mech suffers a +2 movement modifer and a running one suffers a +4. And jumping is a +6. This allows kicking, but makes it far less effective in your average situation.
Punching = Even money to hit. No penalty or bonus. Roll on punch table as usual
Hatchets and Swords = Now roll on punch table. Combined with the nerfing of the kicks, this makes melee weapons actually a solid weapons chocie. It's still difficult to close to melee range, and hard to stay on your feet through the weapons phase in the case that you get there, but if you do, now you get to reap the benefits. Some would say this makes them overpowered. I disagree. it just makes them competitive with non-Physical weapons, which considering their tonnage/crit requirements, they should be.
Mace = As per Hatchets and Swords, but a mech with two hand actuators can choose to not fire weapons in either arm and brace their mace attack. This eliminates the +1 TH modifier and adds a -1 modifier in the case of a missed swing. This makes maces less of a waste of space compared to Hatchets, which is what they currently are.