It is definitely not worth it for a +2 effective bonus.
Why get a weapon that slowly increases from +1 to +5 (since it can't go above 5) when you could just have a +3 all the time?
Even in an amulet of mighty fist, where bonus are limited to +5?
In an amulet of mighty fist, it might actually be worth it, since A) you don't have to pay a +1 at first, and B) you are likely to have multiple attacks (through flurry or natural attacks).
I don't really know if I would use it. Against bosses it certainly going to be worth it, but you loose out against multiple enemies.
Even in an amulet of mighty fist, where bonus are limited to +5?
Yes, I'd rather have +2 to hit and damage all the time, than less until I hit someone 3+ times in a row.
Wow -- I've never seen that weapon property before, but it looks pretty terrible. It probably wouldn't even be worth it as a +1 ability, let alone a +2 ability.
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Even if it were only a +1 property it would only be beneficial if you attacked the foe successfully at least 4 times. It's +0 on the first, +1 on the second, and +2 on the third which averages to +1, which is the same as just making it a regular enhancement bonus. It's only when you get to the fourth that it would be better (averaging +1.5 instead of +1).
As a +2 equivalent, you would need to hit 5 times to make it roughly even, 6 to gain any advantage. And this assumes a +1 weapon. At +2 furyborn it's 6 to break even, and at +3 or higher you literally cannot break even as the most benefit you can gain is +2, which is the same as if you had just made it +2 higher in the first place.
I can see the conceptual niche they were likely trying to fill with this, but it simply falls flat IMO.
EDIT: I could see this property being an okay tool for dealing with foes that have bypassable DR if it were only a +1 bonus equivalent, but not as a +2 equivalent. Even then, the +5 cap means I would likely just add the normal +1 anyway.
The benefit here I see for amulet of mighty fists is to overcome DR. Since this is an increase in enhancement bonus, at +3 you would get cold iron/silver bypass on DR, +4 adamantine, and +5 alignment. The mobs this would help against are the DR mobs that you can still DAMAGE at +0 (if you don't enchant your amulet with a basic +1) but just aren't doing your max damage output. Eventually (possibly by the end of round one if you hit and damage with at least 3 natural attacks (i.e. Dire Tiger)), your enhancement bonus will be high enough o bypass DR (hopefully) at do max damage. I see this helping natural attack fighters in having some way to bypass DR (there are not many options available that don't cost a ton (like a +3 amulet of mighty fists!)
There was a post in one of the threads from shortly after the Ultimate Equipment came out regarding the enhancement bonuses provided by the Furyborn and Bane weapon properties. In short, while the usual rule is that enhancement bonuses cap at +5 "simple" and +10 total, Bane and Furyborn are the exceptions. If I have a +5 Holy Evil Outsider Bane Furyborn whatever, and I'm fighting a Demon Prince, after 5 successful attacks it will have an effective +12 simple enhancement bonus, for a +17 effective total. Against a specific category of enemies, after dumping at least a buffed full attacks worth at the guy.
And even if that isn't the case, that's how I rule it.
The real problem with furyborn is that it bring another modifier (which changes with avery attack and with different opponents) to high level games, when a player of mine tried it on his fighter/barbarian during RotRL it gave him a headache.