This would lead to extra min-maxing, and can be slightly overpowered.
The balance of "half" feats assumes that if one feat grants a special ability and +1 to an ability score, and that this costs the same as +1 to two ability scores, that we can mathematically reduce the value of special ability to +1 to an ability score, or half a feat.
However, this comparison is flawed because feats give a fixed ability score increment, whereas the alternative is two freely-chosen ability score increments that can be assigned optimally. For example:
Take a cleric with Str 14, Dex 10, Con 13, Int 11, Wis 15, Cha 13.
- If they take Heavily Armored, the +1 Strength does nothing for them at this point because their ability score modifier does not increase.
- If they take Keen Mind, the +1 Int will do relatively little because a Cleric does not rely on Int.
- If they take half-feats of Heavily Armored and Keen Mind, they gain two significant abilities in one level, and sacrifice only ability score increments that are useless to them. This is clearly a superior choice to either feat.
Take a high-level fighter with Str 20, Dex 14, Con 15, Int 10, Wis 11, Cha 10.
- If they take Heavy Armor Master, the strength increase does nothing because they've hit the cap.
- If they take Keen Mind, the +1 Int is of little use.
- If they take half-feats of both, they gain both abilities. This is a clearly superior choice.
- Had they spent freely on ability scores, they could have had Con+1 Wis +1. Therefore, two freely-chosen ability scores make this character more powerful than the Str+1 or Int+1 Int mandated by the feats.
Another issue is that you significantly reduce the cost of armor proficiency feats. It may even be possible for a character to take two ranks of armor proficiency at once, which would let e.g. a variant human wizard start with medium proficiency right away, which is not how it's intended.
You also radically decrease the price of Observant, which is already an exceptionally good feat. If I didn't benefit from another point in either Int or Wis, I can now take Observant and another feat. Or, I can take an Armor Proficiency feat and throw in Observant for free.
Allowing half-feats may also allow the character to take a larger number of unique abilities than expected. Increased versatility is valuable to a character.
Yet another issue is that it impedes the thematic meaning of feats. You can now have a character able to wear heavy armor despite being a complete weakling who has not physically gained any strength on his adventures. Historically, there are real-world records of knights would would train for strength and physical fitness while wearing plate armor in order to move around in it well. Letting you get good at armor without improving your fitness suggests it is just a matter of technique, which doesn't make sense thematically.
And an important but subtle balancing factor in, say, the armor proficiency feats is that since a wizard doesn't rely on Strength, it's significantly sub-optimal for him to buy his way up the armor tree because the Strength bonuses won't benefit him very much. This reinforces the important connection between heavy armor users and melee combat.
In short, it's not entirely game-breaking, since feats that grant +1 to an ability score are generally secondary abilities that don't raise your character class efficacy and merely add some useful additional talents. However, allowing half-feats is slightly more powerful than the default, since players will only take combinations that are more optimal than normal, and this will offer an additional avenue for min/maxing.