I think I post my opinions about the matter, before I start an excessive fire spell casting.
I think it's good that they combined TWF and Ambidexterity into one feat. It was exceedingly rare that anyone took only one of these feats, those that don't need the two-weapon fighting part can just ignore it, and if you do lose one hand, the DM will surely overcome the usual penalties to fight with the off-hand overtime (so now your other hand is your main hand). Plus this only occurs in gritty scenarios, where you don't have access to a cleric that casts regenerate on you, and in normal combat you don't use limbs in D&D.
Plus it makes it easier, for we don't have as many different options when fighting with two hands.
That whole "this feat gives me +x to hit" is something The King of the Golden Harry would gladly take away for a small fee. The feat doesn't grant you any bonus, it lessens a penalty. While both a lessened penalty and a bonus will increase your total attack bonus under the usual circumstances, only the bonus will allow you to actually get over the normal maximum. With Weapon Focus (gives a bonus) you will be able to inflict BAB + Ability Modifier + Weapon Bonus +1. With Weapon Proficiency you will be able to inflict BAB + Ability Modifier + Weapon Bonus. Which is the same as anyone who is "inherently" (cause it's a natural weapon or cause his class gives him automatic proficiency) proficient with the weapon.
Plus, Standard penalties for fighting with two weapons are -6/-10, while TWF grants you -4/-4. The "net gain" is +2/+4. If you add it all up, you'll have +6. A wizard who takes Simple Weapons Proficiency and uses two different simple weapons at once he wasn't proficient with before (say, a heavy mace and a light mace), will have +0/+0 with these weapons (not considering two-weapon fighting), while before he hat -4/-4. The "net gain" is +4/+4. If you add it all up, you'll have +8. Gosh! A plus 8 attack bonus, AND it can be used with two different weapons, you aren't fixed on one weapon. That's EVEN MORE than two weapon's fightings "bonuses". OMG! SIMPLE WEAPONS PROFICIENCY IS SO BROKEN. WIZARDS ARE THE NEW MELEE MONSTERS!
This sounds like BS too, but at least the numbers are right. In fact, though, it doesn't hold any water (a fate which is shared with your "TWF gives me +8 on my attacks" conspiracy theory, with the difference that I'm actually aware - or willing to admit - that what I say doesn't make any sense to a sober person).
The second thing, a feat - whatever we call it - that gives you the full strength-bonus to your off-hand attack, is broken, on the other hand. It would mean that you get more out of your strenght with those two wee weapons than the heavy weapon guy gets out of his big, mighty instrument of destruction (tm). You'd get 2x strenght, while he only got 1.5.