Yes, I have played BattleTech on two to three occasions, and discussed the game beyond that. When we played we used pre-defined mechs, to save time over creating our own. Our pre-defined Mechs had lots of weapons each with different range capabilities and, as I recall, some weapons, like missiles, don't work at close range, but other weapons, such as machine guns, only work at close range.
So, I can see the tactical logic of your argument. However, the rules we played, hit location was determined by a table known as an "Armour Diagram" on the targets Record Sheet. Nothing to do with attackers proximity to the Head, or attackers choice of weapon. But there were optional rules that we did not investigate, including heat build-up. Maybe you are referring to an optional rule?
None of our pre-defined Mechs had melee weapons, but, now you mention it, I can see that melee weapons are allowable in BattleTech. According to sarna.net, certain melee weapons have advantage of being better damage than a punch and don't incur heat build-up. And that makes sense to me. But it doesn't go on to say how a Mech, armed with a sword or a hatchet, can inflict cutting or slashing damage (?) on another Mech, which is the point of my comment that these additions are no more than improvised cudgels.
BattleTech Mechs are a bit like Combat Walkers in 2300AD in that they provide a pilot with a piece of armour on legs, equipped out with weapons

. However, 2300AD's Combat Walkers do not appear to have melee weapons of any kind. This is sensible, in my mind, considering the size and tonnage of the opponents armour.