Allowing Fighter Damage Bonus Choice?

Suppose classes with a fighter damage bonus could choose how to apply that bonus going forward?
I first thought of this with respect to the classes that have a fighter damage bonus, melee OR missle. Suppose when the bonus increased to +2, the character could choose +1/+1 instead? A rule would look something like this:
“The character must choose which type of attack will receive the bonus when received, and may not change the choice as he advances.”
This doesn’t strike me as an unfair advantage, but what about full fighter damage bonus classes? The “worst case” scenario is a fighter who allocates all of his bonus to one type, as a dedicated archer or weaponmaster. Then we have:
1st level: +2/+0
3rd level: +4/+0
6th level: +6/+0
9th level: +8/+0
12th level: +10/+0
+6 and above is a little scary, but I’d be willing to try it.
Has anyone else tried this? Thoughts?

I suspect the outcome will be considerably more specialization, biasing towards melee for high STR fighters.
The key to the fighter damage bonus is its effect on Cleaves.
1st level fighter (STR16 = 1d6+2 + f.dmg.bonus) v. 1HD orc (5hp)
1d6 roll of 3+ cleaves without fighter damage bonus (33% of not cleaving)
1d6 roll of 2+ cleaves with +1 fighter damage bonus (16% of not cleaving)
roll of 1+ cleaves with +2 fighter damage bonus (always cleave)
At 6th level:
6th level fighter (STR 16, +1 sword = 1d6+3 + f.dmg.bonus) v. 3HD bugbear (14hp)
F.dmg bonus is either +3 or +6
Fighter can’t cleave bugbears in first scenario, can cleave on 5-6 in 2nd scenario
By mid-levels, your fighters will be whirling dervishes of destruction in whatever they’ve specialized in. Less specialized fighters will seem less and less capable of cleavery.
So it depends on whether those are outcomes you’d want.

Also ranged cleaves are capped at 4.

Great comments, thanks!
In some settings or one-shots, awesomely cleaving fighters could be interesting …
I’m still interested in exploring some flexibility in my regular campaign (and, as Judge, I’ll ensure intelligent opponents specialize themselves or attempt to exploit over-specialization, as appropriate).
I’m thinking of experimenting with allowing the choice I mention at levels 6 and 12 only.
That leads to, “at worst”:
1st level: +1/+1 +1/+0
3rd level: +2/+2 +2/+0
6th level: +4/+2 +2/+1
9th level: +5/+3 +3/+1
12th level: +7/+3 +3/+2
I see the cap on ranged cleaves as part nod to realism, part balancing mechanic versus the movement limitations on melee cleaves.
(Tinkering with these limitations in some settings could be interesting, as well, be it a “weapon of the ancients” that throws slugs or beams, or John Carter vs a Green Martian horde …)