Same as FDru, except it goes a bit further. Essentially, not having an item handy affects the choices of what I'm even considering to take to a run, whether I'm willing to risk time with, say, a dwarf, or go for a more certain experience with something which synergizes with the items I have. It's often impossible to know whether I even want an item lockered before I locker it, while I always know I want the stuff that's already there. The longer a profile goes, the more this affects my temporary playing habits.
Sometimes I'm in the mood to experiment with a specific thing, being forced by the game to do something else is hugely annoying. Failing a vicious 2-3 times and coming up with an item that would help me, breaks the mindset I was in, and if scumming for it takes long enough, it affects my further efforts immensly. Avatar mentioned this with piercing wand and daemonic library recently, and it resonated strongly with my experiences.
Many PQI runs have a non-sinergistic race/class/badge/dungeon setup, which having an item handy would change in an instant, from "would take a major perspective shift" to anything between "skippable" - "interesting and novel". Many races and classes become way more interesting with items that are niche (as in the case with Blue Bead). Scumming for that item with a tinker requires revealing an entire map, scumming with a transmuter has me looking at less shops.
The game offers enough runs to make (over (edited after calculation) 700 (!!!) hundred even if I manage to get "everything" without redundancy), and while I love quests, feeling forced to do a run with all the possible ones looking at me tantalizingly is very offputing. This increases the more time I spend playing in the course of a playthrough - and at the point where I'm "in form" enough to do vicious runs on a regular basis, justifying doing redundant time-consuming runs as a time investment becomes increasingly impossible.
Relockering a vicious reward means that I have to do a specific vicious run - if I want Naga Cauldron I need to do Naga City, even if I'd be more interested in investing my time into investigating, say, Demonic Library. It's why I have only one run of daemonic libaray - I did 3 everywhere else without vicious rewards, to test their challenge level, but I waited with the last dungeon untill I've ground a locker slot, to avoid having to do that dungeon more times than I want. Untill this playthrough, I've played Namtar's Lair about 2-3 times total, to my memory - I'm not at all interested in playing that place other than lockering the ward, and removing it from my locker would mandate doing something I've never felt inclined to do off my own free will for a year.
As for why not pick stuff up on regular runs - well, I don't even use the prepped items all that much, I use them to keep my options open. Items I bring back from a run get judged against the items allready in the locker - and if they're more niche or easier to scum for, lockering them would affect me during the prep screen in a more limiting way, or increase the chances I'll have to invest more time into looking for whatever I took out.
Not to mention that many things which I would love to have available are also things which get converted on a regular basis, and I never actually finish a run with them in my inventory. I'm big on troll heart, bloody sigil, mage plate and such. Even if they weren't judged in "effort/need to relocker" against stuff that can't be beat in that category, I rarely ever see them even in the backpack. That's a bit of backpack feedback I was meaning to give but kept forgetting about.