Wizards can do pretty high damage and have higher toughness than DHs, so in theory they should do better in higher Greater Rifts. At least that's my theory for multiboxing only. But, the main problem is CC and pets. DHs have cold damage that will slow everything. Even 1 DH will keep everything slowed (I prefer 2 DH with cold) . And to make it even better, they have 4 autocast pets that will distract mobs so DHs can go to a safe spot and wait til everything dies. Since they have high burst damage, they can afford staying without moving forward to wait til things die.

Firebird Wizards lack burst damage, don't have pets and CC is not great. Skills have long cooldowns and slowing things is prolly not the best idea since Firebird gamestyle requires mobs to be chasing u and die 1-1.5 screens away from DoT. If they remain stunned/slowed, then u may go out of range and the infinite DoT stops, causing them to not die. Sure u can stick around and wait til they die, but then u will fail the rift anyway. This build requires u to keep moving forward or u won't have enough time. U cast your Blackhole, Apocalypse and leave a Hydra ahead and go to the next pack. Not even stop for elites, just gather 1-3 packs (asuming affixes are not a huge pain in the butt) and DoT all.

The idea of having a WD is that u can still move around, cast your DoT safely and keep moving forward. Mobs will still chase u and keep up with your pace, but the WD will prevent anything from coming too close and hit u. That's why I decided to go with that combo, otherwise, if u go with 4x Wizards, u might run into survivability issues. If u have Illusionist passive, that will cause horrible dsync issues cause not all wizards will get hit at the same time, causing your teleport to be off cooldown at different times for each wizard. Without Illusionist, teleport is limited to your CDR and may not save u in most cases. I rather replace teleport with Familiar or anything that adds more damage.

4x wizards i's doable, but I don't think it will be more efficient than 4x DHs cause u will be running and kiting all over the place and 1 or more wizards will die at any time. U need something to distract mobs and CC them to the point u can free cast and let them chase u til they die. U can try slowtime with mirror images and try to not go too far so things still die, but not sure how efficient this will be. It's something I will test later on.

A SMK WD will boost the party DPS and provide the kind of CC that wont interfere with Firebird gamestyle.