To those who believe action points destroy roleplaying: Congratulations, you have disproved Eberron. Check your bookshelf, seriously, there should just be a pile of ash where your Eberron sourcebooks used to sit.
To those who believe that action points grant rerolls: They don't. They grant extra actions.
To those who want rerolls replaced with static modifiers: This could work, but you wouldn't get the same odds. The value of a reroll scales based on the difficulty of the initial roll in a manner different from that of a static modifier.
For example, if you hit on an 11+, you have a 50% chance of hitting. Giving you a reroll increases your overall chance to 75%. You would have to grant a +5 static modifier to accomplish that.
But if you hit on a 16+, which is a 25% chance of hitting, a reroll improves your overall chances to about 44%. You'd need a static modifier of about +4 to accomplish that.
And if you hit on a 19+, which is a 10% chance of hitting, a reroll improves your overall chances to about 19%, which is the equivalent of a static modifier of +2.
Things change similarly if you move the chance of hitting downwards.
Meanwhile, rerolls are easily applied after you know the outcome of your attack, and they don't rely on metagame knowledge to do so. If you miss, you just ask to reroll the attack. This gives you a "I saved the day!" feeling when it works. You don't get a similar feeling from declaring that your next attack roll is going to be +4 due to a per encounter ability, then rolling.
And powers that add static numbers after the dice have already been rolled have been tried in the past, and while they weren't horrible, they did rely a bit on metagame reasoning. A player who knows how much they were hit by is better off using something like Zephyr's Dodge from Book of Nine Swords, because they can make sure to always use it in a situation where it will result in an avoided attack. This turns the power into an "always works if you pay attention to the numbers" type situation, instead of a randomized one.