Well, seeing as this is a house rule, it's entirely up to the DM, obviously.
The way I'd look at it tho is...
why is the house rule used? What is its purpose? In this instance, it's a house rule that is designed to remove the +1/2/3 bonuses to character attack rolls. It's not because the word 'Expertise' is offensive, it's the effect that such a feat gives that is disallowed.
So, is this a feat that breaks the idea of banning +1/2/3 to attack roll feats? Absolutely.
Moreover, I tend to look unfavorably at players who try to break the spirit of house rules by trying to use a technicality as 'It doesn't have Expertise in the name!' as if that is somehow relevant to the point.
I understand your desire for a simple feat that gives an attack bonus. You simply have to put trust in your DM that he won't put you out of your element for attack-probabilities. To be honest, Expertise feats are not, despite what people claim, necessary to attain 50/50 attack rates... you start off, and stay, ahead of the curve.
But even if they are, the DM has more than enough ability to adjust monster encounters to compensate should it be a problem.
Remember, you're already getting it for free with every weapon! The vanilla version, at least. I reduce monster defenses by +1 per tier, and no feat is required. I also give an additional +1 for describing attacks, but that's just gravy to encourage cool descriptions.
Thanks for the quick feedback, everyone. I agree, it's an expertise feat. And Blood Jester is a spectacular player who really does have awful luck with dice. I once watched him fail something like 6 saves in a row against a stun effect. Yikes.
Oh hey, like this!
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There remain ways in the game, however, to address YOUR issue, so that you can play the character you want. You are expressing a desire to increase accuracy, and this is a very fine goal. My suggestion is to play a character that either gives you inherent bonuses to accuracy, say a thief or fighter, a race or class that allows you to change misses into hits, say essentials human, elf, avenger, or deva, or a class that allows you to take advantage of the non-AC defenses system, say a wizard, sorcerer, or whatever, or a class that doesn't rely on hitting to be effective, like a warlord or Con/Cha hammer rhythm battlemind.
If you play a deva or elf avenger, you won't miss Expertise one bit.