From a strictly RAW core POV, here is what we have so far:
1a) An Unarmed Strike is not a Natural Weapon. It follows virtually none of the Natural Weapon rules. Monks do not have a Natural Weapon and hence do not qualify for the feat in the first place.
1b) The counter position is that spells like Magic Weapon indicate that Unarmed Strikes are Natural Weapons.
2a) An Unarmed Strike can be considered a Natural Weapon for spells and effects, but for no other purpose. A feat prerequisite is a different purpose and there are no rules that feat prerequisites are either spells or effects.
2b) There does not appear to be a counter position to this other than 4b below.
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4a) A feat is not listed as an effect either. There are no rules in the feat section concerning feats as effects or having effects. Feats are listed as having benefits.
Note: There is one table qualifier in a different section of the rules that specifies that the feat description defines its effect. However, this is ambiguous as the feat description describes prerequisites, benefits, normal limitations, and special facts. None of these are specified as being effects and some of them do not make sense as effects. Not only that, but the general rule is that text overrides table entries and since there is no text in the feat section concerning feats being or having effects, it would be extremely difficult for a DM to find this obscure table entry in a totally different chapter of the book and come to the conclusion that it is real support for a INA allowed POV (In fact, this particular quote was first introduced to the discussion by me a few weeks ago. Search the Internet. Nobody even knew this obscure little sentence even existed in the rules with regard to the INA discussion until I mentioned it the other week, even though the INA Unarmed Strike discussion has been going on for years). This does not change the fact that the sentence exists, but it does illustrate that the sentence does not appear to be an intent by WotC that feats are or have effects. Instead, it is meant to illustrate what the action type of a feat might be with regard to the Action In Combat table. Using it to illustrate that feats have or are effects is taking it out of context of that table.
4b) The counter position is that the word effect means the English definition of effect. Hence, anything in the game that affects anything else is an effect. This includes BAB, saves, alignment, etc. With this interpretation, a feat or feat benefit could be or have an effect and hence, a Monk could apply INA to an Unarmed Strike. This counter position also indicates that the feat description defines its effect sentence gives feats the carte blanche ability to be or have effects, regardless of the term effect not being within the Feat rule section.
5a) The monster feats are listed as typically used only by monsters and are also found in the Monster Manual. This indicates that not only DM caveat is required to use them, but that the intent of them is for monsters only unless a core rule specifies otherwise.
Was there any major points I missed? Did I misrepresent any of these points?