I know, from experience, that both these things are false.
An equipment list isn't a procedure of play. The Matt Colville video that was linked to upthread explains the procedure of play that the classic D&D equipment list supports - it is, roughly:
(1) Prior to actual play starting - in the prep phase - players add stuff to their PC equipment lists;
(2) During actual play, the GM describes/narrates (whatever verb one prefers can be inserted here) complicated situations to the players. These situations are architectural or similar sorts of challenges to the players - pits, chasms, locked doors, weird pillars, wonky slopes, etc;
(3) The players describe how their PCs deal with those challenges, and as part of that describe how the equipment on their PC equipment lists helps. with this;
(4) The GM makes a decision about how this pans out, doing their best to be true to everyone's shared imagination of the situation and everyone's shared knowledge of how shovels, poles, wire, string etc behave when used as improvised tools.
In other words, the reason for the classic D&D equipment list is
because it impacts pay when
play follows the above procedure.
You can have plausible imaginary worlds while using different procedures of play. I'll offer up my 4e D&D play as an example. In that play, the PC equipment lists that players create for their PCs don't figure in play as prominently as they do in classic D&D dungeoncrawling play. On the other hand, different things do impact play that do not impact play in that classic play (for instance, PCs' loyalties and their hopes for the future of the cosmos).