I don't understand that logic. If a spell description was written "As part of casting this spell, you must make a melee attack with a weapon against one creature within range, otherwise the spell fails. On a hit, the target suffers the attack's non magical bludgeoning/piercing/slashing damage effects" would that not matter to you? That to me is the normal effect of a mundane weapon attack.
Well your modified version would do a few things:
First, you could argue that if you were using a magical weapon which had a damage type, say fire, the spell would specifically stop the magical damage type and cause you to only deal a normal damage die + modifiers worth of damage. This is because the damage type is from the magic and would be replaced by the weapons base damage type (slashing, piercing or bludgeoning) as you called out.
Second, any effects of the attack beyond the specific non-magical bludgeoning/piercing/slashing damage would no longer be applied. Like blindness on hit / save vs an effect and so on because that too is granted by the magic from the magical weapon.
All that being said however, I'm not even convinced that your custom version would stop the attack from bypassing since the source of the attack is STILL a spell. You would need to specifically call out that the attack "does not bypass resistance and/or immunity to non-magical attacks."
But again you don't seem to understand (and I say this based on your custom text) that the errata isn't about the effects the attack might have on a
hit, or
effects in general or
damage dice,
damage type etc... All that matters is the SOURCE of the attack. If the attack is from a magical item, it bypasses no matter what the attack's effects, damage dice, damage type, etc.. is unless the wording of the attack specifically states that it does not. GReen Flame Blade does not specify that the general rules for bypassing resistance and/or immunity don't apply. It only talks about the effects of the attack. The source of the attack is not the effect of the attack. That's wrong.
EDIT: The moment you cast a spell which let's you make an attack, regardless of any other factors (unless it's specifically called out like I mentioned above), your attack
will bypass resistance and immunity to nonmagical attacks. That's a fact post errata.