Given that every spellcasting class in 5e has its own spell list, it makes perfect sense to me that a Witch PC class would have the same. Given that, the player is free to flavor this as the Witch "getting their feet wet" with the variety of traditions before selecting one in which to focus/specialize. Players with a clear image of what they want their witch to be like/the "type" of witch they are going for (fate-weaver/fortune teller, enchanter, conjurer/fiend dealer, nature healer, etc...) the player is free to simply select 1st and 2nd level spells off the Witch Spell List that are in line with that flavor, and then the added bonuses/benefits coming in at 3rd with their "formal" tradition choice/initiation.
It's exactly how the wizard & druid class is composed. Which makes, to me, the most sense for the witches to be in line with. Clerics select a domain at 1st because 1) they need to have a deity as part of their core identity/character options and 2) they are receiving bonus (not necessarily "Cleric") spells in line with that deity/domain choice. Sorcerer's select a Bloodline at 1st because that is the core/root of their magical powers. Makes sense that /has/ to be determined/should be part of the character's identity from 1st.
For Witches, as the brilliant descriptions/flavor has been created of this class of gathering, learning, piecing together with passed down lore and "practical" magic ability, the tradition choice at 3rd level makes complete flavor sense and is in line, to my view/thinking, with the construction/structure of 5e classes, perfectly.