The permanent modifier to all allies' rolls appears over the top to me. I doubt this was the intent, and honestly I'm not going to search the book to point to rules pages; but it would be a freakishly strong ability that the halfling should never, ever, except to save himself from certain death, give away against a one-shot luck burn. Everyone getting even only a +1 to all their rolls all the time, is wayyyy better than the halfling getting +5 or even +10 to one roll once. Some will argue, "it depends on the roll"... Well, that's B-S, because statistically, that permament +1 is going to improve all actions so much that getting one sure success through luck burn by the halfling is not going to outweigh that 5% increase in success of all actions by all other PCs.
If your player tries to argue that rule, simply say "no". Period. "I'm not going to accept a permanent ambulatory bonus-giver into the game because that's not how I interpret the rule. If you feel otherwise, you can run a game for us, and we'll try hard to find ourselves a lucky halfling
Obviously, if the halfling is Lawful, it would require dire circumstances to cause him to short the entire party for a one-shot roll on his own behalf. But if the halfling is Neutral or Chaotic, then conserving his luck in order to share out his modifier would be out of character. As a judge, I'd be more than happy to say that any halfling so intent on using his luck on behalf of others would essentially be denying himself luck -- meaning that monster attacks and traps and spells might be more likely to target him, eventually forcing him to augment a save with a luck burn. And if that halfling were playing against alignment to boot, I'd magnify the effect.
The potential effect on party dynamic could be fun too. I would subtly (or not so subtly) encourage the other players to behave in an overprotective fashion toward the halfling, so that he might find it constantly chafing that they won't let him be the one to search for treasure, or to parlay with the black knight ... or even to go out after dark, lest they lose their cherished bonus.
I'm not too worried about my players colluding to min-max the use of the bonus, and if they do become over-dependent on it, that just gives me a story hook to create an adventure in which the halfling gets cursed and the party has to quest to restore his luck. Or one in which nefarious strangers hear of the miraculous lucky boon in this individual halfling, and kidnap him in hopes of making use of his good fortune for their own purposes.
With all that said, I agree that the "ambulatory bonus-giver" interpretation probably founders on the simple disproportionality of the whole party having a (potential) +3 to all damage rolls. That's an enormous advantage, and would require the judge to retool a lot of encounters, especially at lower levels where the monsters don't have that many hit points.