They're not magical
But first, let's clear something up: Weapon Bond doesn't turn a weapon into a WCMFTPOOR. That's not stated anywhere in the description.
The rules say precisely what they mean
The phrase "...considered magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage" means precisely that, nothing more and nothing less. If the weapon were magical, the text would say so. If it were magical for any other purposes, the text would say so (and it would've been far simpler to state it that way).
Granted, there are places where the rules rely on the everyday English and some ambiguity sneaks in, but this isn't one of those cases.
Here's an example of a related rule that's defined in a similarly pedantic way: immunity or resistance to "bludgeoning, piercing, and slashing from nonmagical attacks not made with silvered weapons." If you hit a werewolf with a torch, it'll take fire damage; swinging the torch was a nonmagical attack, but it didn't deal bludgeoning, piercing, or slashing damage. If you push a werewolf off a cliff, it takes falling damage; falling isn't an attack. And of course if you attack a werewolf with a nonmagical silvered weapon, it takes damage.
The text behind the rule is a mouthful, but it's written that way because the authors want it to work that way (1, 2, 3). They could've written "nonmagical damage" to cover things like torches and falling but they didn't.
Monks do not become magical creatures at level 6
Monks gain a class feature called Ki-Empowered Strikes that lets them treat their unarmed strikes as MFTPOOR.
Starting at 6th level, your unarmed strikes count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.
There's a few things worth pointing out here:
- This is essentially the same text that's in Pact Weapon.
- Unarmed strikes are not weapons.
- Ki is not magical for rule purposes.
(1, 2, 3)
- Even if Ki were magical, it would be a huge stretch to say the Monk's entire body becomes magical.
That third point requires more explanation. Sage Advice addresses this in the question "Is the breath weapon of a dragon magical?". The answer is a bit long, so I'll quote the most relevant part:
But our game makes a distinction between two types of magic:
- the background magic that is part of the D&D multiverse’s physics and the physiology of many D&D creatures
- the concentrated magical energy that is contained in a magic item or channeled to create a spell or other focused magical effect
In D&D, the first type of magic is part of nature. It is no more dispellable than the wind. A monster like a dragon exists because of that magic-enhanced nature. The second type of magic is what the rules are concerned about. When a rule refers to something being magical, it’s referring to that second type. Determining whether a game feature is magical is straightforward. Ask yourself these questions about the feature
- Is it a magic item?
- Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
- Is it a spell attack?
- Does its description say it’s magical?
If your answer to any of those questions is yes, the feature is magical.
It doesn't break anything
In terms of Rules As Fun, without any Unearthed Arcana material, a melee Warlock is generally less effective than an Eldritch Blast Warlock. The Eldritch Blast invocations are so powerful that it's almost difficult to justify using anything else. Anything that encourages diversity and lets players play how they want is a good thing. Let Blade Warlocks have their +1 weapons.