D&D didn't invent the paladin archetype. Romantic authors of the high middle ages did, and it has been reinforced and perhaps in some ways developed over time since then.
When I play a paladin I have zero interest in playing a divinely powered mercenary. In fact that is the interpretation I place on the sort of paladin you and others have described upthread, one who receives divine power only provided that s/he sticks to a code that is, from the point of view of the universe, arbitrary - arbitrary because, from the point of view of the universe, there is no reason to be LG rather than (say) CE.
When I play a paladin I play a character who believes in the reality of providence, and hence disavows all dishonourable and unjust conduct. Claims that evil must be done so that good can ultimately triumph are, for the character I am interested in playing, flawed for two reasons: first, they are empirically false; second, they are betrayals of faith in that divine providence which ensures that those who act morally will not be betrayed.
In what way are these ideas different? Is it because one has a hard written list of rules they must abide by (The Paladin's Code) while the other presumably does not? Yes the code is arbitrary but so are all codes of conduct, they all draw lines at particular points for various reasons. The Paladin subscribes to a code of conduct and is blessed by divine providence for it, however there are also Blackguards and Evil Clerics who are also blessed by divine providence for their behaviour.
Unless you're running a game where only Good gods exist, or at least only they bestow blessings on their faithful, the Paladin must accept that he lives in a world where Evil has power, where there are rewards for being dishonourable and cruel, and he must stand by his code in spite of that.
This is where mechanical alignment makes Paladins and Clerics more interesting (to me) because there is now the possibility for temptation, corruption, and ultimately a fall from grace. This can't happen in a descriptive alignment system because either A) the player never accepts that their character is acting out of alignment and refuses to change, or B) it's a scripted event and loses any kind of tension or drama.
In mechanical alignment you can force a player to weigh the benefits of holding to their alignment against practical concerns. Do we poison the duke to end a battle before it starts or do we meet them honourably on the field? Do I grant mercy to my enemy knowing he might go on to do evil again or do I take it upon myself to be judge, jury, and executioner*? You can't give these decisions any weight in a descriptive system because the players is never in any danger of losing anything from acting out of alignment.
*This assumes the enemy has stopped fighting and pleaded for mercy.
These are the sorts of characters I want to play. The D&D paladin captures them very well mechanically - a warrior who is divinely bless, can heal with a touch and smite his/her enemies - except that the alignment mechanics get in the way, by either ruling out from the get-go the cosmological world view that underpins the class, or (on a different approach to them) turning the character more-or-less into the GM's puppet.
In what way does it rule out the cosmological world view? As for turning a character into a GM's puppet, the GM has much better tools than alignment if that's what they're going for.