I *think* it's because (most) undead are supposed to be fearless, and only the divine can make them "remember" what it is to be afraid of death again. Therefore, Turn Undead.
A blessed sword could, as a magical property, be used to turn undead, but the plain "deal holy damage" types would only cause concern to inteligent undead - and even then, it wouldn't be any different than an adventurer being threatened by monsters.
Well, by that logic then I'm much like the undead.
I'm fearless too until someone puts a sword to my throat or threatens me with a loaded crossbow.
A slug is fearless too but put some salt or fire in its path and it will try and go another way.
I don't understand the idea of a 'plain' deal holy damage weapon. If the weapon (in 4e terms) does radiant damage then I don't think it needs any additional rider/ability to be considered a threat by anything. A slug or an ant recognizes fire and I'd think a creature vulnerable/weakness to holy/radiant damage would recognize the existence of the item.
You can threaten or train even things that most people would consider unintelligent which means that you can in some way communicate with these creatures (even zombies and skeletons can be communicated with otherwise a Necromancer would never be able to even get these things to follow them much less stand in a straight line for a minute).
Treating a turn check as an Intimidation, Bluff, or Bribe check offers some interesting possibilities.
1> It is something that many classes might be able to attempt with training and having the right item to back up the threats. You might need something that shows your ability to cause radiant/holy damage (whether this be a spell like cure wounds, a holy weapon, or a scroll/book of holy writs) and the ability to communicate with undead (part of a cleric's normal skill set as they use prayers during burials to set the spirit at ease).
2> An evil cleric would just need to do the opposite to attempt to gain service from a creature (though any class that could get the pieces together could attempt the Diplomacy or Intimidation to get a result).
3> When it comes to Intimidation there is usually a fairly clear link between level and their ability to cause harm (grant aid) which would reflect the growth of ability to affect tougher creatures and more intelligent opponents. If you choose to Bluff then you might only hold the upper hand in a situation until your opponent learns of the weakness of your powers or the source of your powers (lose the holy sword and the vampire will be having you for supper).