This was difficult! I decided to look at it less as what three animals I would remove persay, and rather what species I considered to make the strongest four habitat species roster. The result:
South-east Asia Pack - Sun bear, binturong, proboscis monkey & north Sulawesi babirusa (dhole, tapir & clouded leopard removed)
North America Pack - Cougar, moose, California sea lion & American alligator (beaver, prairie dog & fox removed)
Wetlands Pack - Platypus, capybara, Asian small-clawed otter & red-crowned crane (lechwe, water buffalo & caiman removed)
Grasslands Pack - Red-necked wallaby, nine-banded armadillo, maned wolf & emu (hyena, caracal & wildebeest removed)
Arid Pack - African crested porcupine, dromedary, addax, black rhinoceros (wild ass, sand cat & gazelle removed)
And for what I’d add to scenery packs to turn them into animal packs:
Arctic Animal Pack - Mountain hare, wolverine, musk ox, viviparous lizard
South America Animal Pack - South American coati, greater rhea, Patagonian mara
Australia Animal Pack - Short-beaked echidna, greater bilby, perentie
Aquatic Animal Pack - Pig-nosed turtle, mute swan, Australian pelican
Africa Animal Pack - Hamadryas baboon, helmeted guineafowl, grey-crowned crane
Europe Animal Pack - Wild boar, beech marten, white stork
Conservation Animal Pack - Golden lion tamarin, numbat, radiated tortoise
Twilight Animal Pack - Aye-aye, Reeves’ muntjac, common brushtail possum
Tropical Animal Pack - Red-rumped agouti, Geoffroy’s spider monkey, lowland anoa
Oceania Animal Pack - Nene, kagu, Goodfellow’s tree kangaroo