Where Warrant suffers relative to other options is against utility creatures, mainly mana creatures like Llanowar Elves and Incubation Druid, but most control players are happy to see those cards because they can focus their answers on the big threats with little threat of dying from the cheap cards
PT (UTC-08:00) on the ending date shown unless otherwise noted
That being said, Rat decks have existed for a while, with cards like Marrow-Gnawer turning a single Rat into an army
As white typically runs creature buffs this has good synergies within the kinds of places you might want it
These include cards like Blood Tyrant (drain, +1/+1 counters), Dragonmaster Outcast (5/5 dragon tokens), Indulgent Tormentor (draw, drain), Sin Prodder (draw, drain), Thassa (scry), Twilight Prophet (draw, drain), Wildfire Devils (reanimate spells), Skyline Despot (5/5 Dragon tokens), Avarice Amulet (draw), Extravagant Replication (clone), and many many more