Blinktwice's page

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Artifacts are unusual magical items, and they are very difficult to destroy. A bonded item loses all its properties if the owner bonds a different item (even those it had before being bonded), so allowing them to be bonded would be an easy and low cost way to destroy artifacts. I would strongly suggest your GM not to allow that (theoretically, the rules allow it).

That said, some minor artifact, like the Staff of the Magi is a borderline high powered magical item and can exist in multiple exemplars, so allowing them to be bonded isn't that problematic.

P.S: "A bonded item loses all its properties if the owner bonds a different item (even those it had before being bonded),". From what I recall, what happens to a bonded item when the owner dies was discussed in several threads, and there was an official ruling, either in one of SKR's comments or in a FAQ, but in a fast check of the CRB FAQs, I haven't found it.
The Wizard ability says that the item reverts to a masterwork item, but there is wiggle room to argue that it reverts to its former abilities. It is a GM call. I would almost certainly do that if I allowed someone to bond a major artifact.

Additionally, depending on the artifact, there should also really be consequences. Most artifacts are deeply connected to beings of power, or times of great historical significance. If you're connecting yourself to something forged by an Empyreal Lord or the Outer Planes, for example, you might be drawing the attention and influence of real power.

A Staff of the Magi and the like is probably fine though.

To my knowledge as well, there is nothing RAW preventing you from binding any magic item or bonded artifact you want as your bonded item. If anyone knows differently, please feel free to correct me.

My group actually had this exact issue pop up, with Dagon wrapping himself in an Antimagic-field to attack a city.

Our consensus, after about an hour of debate, was that anything Mythic could ignore an antimagic field. The basis for this was that Mythic powers can create artifacts (https://www.d20pfsrd.com/alternative-rule-systems/mythic/mythic-heroes/#Le gendary_Item_Ex), so Mythic powers, by default, have to be on the same tier as artifacts if not higher.

So Dagon himself, as a Mythic-tier creature and demigod, was immune to anti-magic field, but any of our Mythic powers, equipment or spells that had Mythic enhancements was also immune. Made it a fair bit of fun, since the party wizard had to be even more creative than the norm about what spells to Mythically empower, and it made the party feel more important since it gave a reason all the NPC's in the city were basically helpless against something with a stat block.

Except for one NPC ranger with Clustered Shot who ended up taking off about 100 of Dagon's HP, I guess.