This is also useful in HC because you can make one with your class cheat death passive and then you'll have that straight from level 1 for the levelling process. Hellfire amulets are equippable at level 1. If you have some Hellfire mats, you can make a few Hellfire amulets. And the mats aren't necessarily wasted, if you get lucky you might get yourself a useful class-specific ancient weapon for your new class.

I mention this because using something with a useful legendary power can speed up the levelling process. So you can make a weapon for your new class on your main character.

you can upgrade flails/bows/fist weapons/mighty weapons/scythes on another class). Or, if you were going to do it on your new character anyway, you can upgrade class-specific items on other classes (e.g. My usual strategy is a Gem of Ease in a level 70 ancient weapon with mainstat + vit. You can use it as an augment later once you don't need it anymore. If you're worried about taking the extra time to level it, it's not wasted. It speeds things up a little bit at the lower levels. If you can get it higher than 25 without too much effort, go ahead.

Diablo 3 leveling gem of ease