My problem is that it is [i]very[/i] hard to write any alternate version of a canon Servant that's any good. Unless they can be summoned in multiple classes, in which case you could write them as their alternative class. And... Saber is kind of my favorite character in the whole Nasuverse so I kind of don't like the idea of changing her but that's not exactly the best reason.

On top of that, Noble Phantasms are something the Servant is known for, or a symbol of what they're known for. With Cu Chulainn, for example, his Noble Phantasm is Gae Bolg. Gae Bolg is the weapon that he is known for wielding in legend.

In line with that, Arturia's Noble Phantasms are Excalibur and Avalon(Invisible Air only kind of counts). These are the two best-known artifacts associated with King Arthur. It's the same with other Servants. Lancelot has his acts as a Knight, and his sword Arondight.

The only case off the top of my head that's different is Gilgamesh, but he's the first Hero so his circumstances are a little different in that respect. And his Noble Phantasms are still somewhat associated with his legend and position as the first hero. Well, Enkidu is much more direct since it's the chains used to kill the Bull of Heaven named after his best friend but yeah.

Basically coming up with an alternate Noble Phantasm for a character that has been used in canon that does not fit into other classes that makes sense is not easy.