Magically enhancing unarmed attacks, such as with fiery fists, is a valid fantasy trope. It can and should exist in D&D for players who find such options appealing.
The convoluted ‘errata’ seems unrelated to gaming balance, since Flurry would deal the same or more damage by magically enhancing the weapons rather than the bodyparts.
I don't think it makes less sense personally.
Hands aren't weapons, even if people trained in unarmed combat are considered weapon by the modern legal system. I just watched a Variety Youtube with Olivia Munn and Jackie Chan where they responded to Twitter questions. one question was about dealing with knife attacks while you are unarmed. Jackie gave a realistic answer on how to best handle them, but his realistic advice was to scream and run from someone if they have a knife and you don't.
Fun video that I'd recommend just because Jackie Chan is great!
There are also ways to magically enhance your first to be fiery... in the Monk class.
- Way of the Four Element's Fangs of the Fire Snake. 1 ki = fire damage instead of bludgeoning on your attacks for the rest of the turn (so all attacks, bonus action attacks, and reaction attacks), increases your range to 10', and you can spend 1 more ki to deal an extra 1d10 fire damage per hit.
- Way of the Sun Soul's Radiant Sun Bolt. Make any attack deal radiant damage that uses your monk martial arts die + Dexterity for attack and damage, and has a range of 30'. Spend 1 ki to do two more attacks like that with a bonus action (kind of replaces Flurry)
Why does "Unarmed Strike" need to appear on the weapons table dealing a flat 1 point of bludgeoning damage and then enhance it with a 3rd level Concentration spell to add 1d4 points of elemental damage to it when you can just be a Monk and do the same thing but with more damage per hit from the unarmed strike & from your monk abilities?
Either of the options above will be able to attack 4 times in a round between action & bonus action dealing 1d6+Str/Dex at range from 5' to 30' + 1d10/ki spent on the Way of Four Element's option. They can do that for 3-5 rounds per battle and get it all back on short rests.
A non-Monk brawler who gets his fists enchanted is going to be maxing at 3 attacks per round if you let them make unarmed strikes as bonus action attacks via Two "Weapon" Fighting. and 1-1d4+Str +1d4 elemental Damage from their friend's concentration spell.
Sorry, there ways to do a brawler build, and there are ways to do all the things people are asking for, even with the Errata.
