What are the consequences if wizards can cast unprepared spells from their spellbooks?

It’s a staple of the fantasy genre: faced with an obstacle the barbarian can’t punch his way through, the wizard flips through his spellbook until he finds the perfect spell. He reaches into his component pouch, withdrawing—somehow—exactly what he needs, then casts a powerful spell, surprising the heroes and allowing them to continue on.

Wizards don’t get to do that in 5e. They prepare so many spells per day out of their spellbook, and unless the other spells within are tagged ritual, they don’t get to see use until after the next long rest.

I want to house-rule that a wizard can cast unprepared spells from their book in the absence of exigent conditions. If I have time and space to crack out my spellbook, being disallowed from mage armor, disguise self, or jump without [8 minus sleep] hours of study feels arbitrary. What about the game changes, especially balance-wise, if wizards are allowed to cast unprepared spells from their spellbooks?

Note: this would be different from [ritual] spell casting from the spell book. In this proposed scheme, casting an unprepared spell would still require slots.

[RAW| How can a Demilich use staves, scrolls, etc., and study their spellbooks from a distance?

3.5’s Demilich has the ability Phylactery Transference:

Headbands, belts, rings, cloaks, and other wearable items kept in close association with the demilich’s phylactery transfer all their benefits to the demilich no matter how far apart the demilich and the phylactery are located. The standard limits on types of items utilized simultaneously still apply.

I have a wizard demilich that has an extremely well-guarded phylactery way over that-a-way, and part of the phylactery’s protection involves the lich simply not visiting it any more than absolutely necessary, lest some freak combination of bad timing and a divination spell reveal its location or defenses.

However, the lich still wants to be able to use staves, scrolls, wands, and rods, and wants to study their spellbooks every night so they have their wizard spells available the next day. Ideally, they’d like to use the odd feather token or other one-shot wondrous item, with bonus points if they can access storage near their phylactery (eg., so their skull form can appear without any treasure, but can still pay for a night at an inn if they so choose).

They’re a 21st level wizard with 2 open non-epic feats and 500,000 gp to spend on magic items for this purpose. They do have Scribe Scroll and Craft Wondrous Item already, and crafting doesn’t cost XP (for the players, either). They also have an augmented Handy Haversack (with plenty of extra storage in the main area). They can also take levels in non-wizard classes, so long as all of those levels increase their wizard caster level (eg., taking levels of Loremaster is acceptable, but Eldrich Knight is out).

I’m looking for a RAW-compatible option for this recurring villain to have access to their non-wearable stuff while keeping it away from the players for now. If the PCs find the lich’s stash, which will include a journal functionally detailing their character sheet, the full ability of the lich to stay away from their phylactery for years on end must make sense. Whether the PCs can use any of the gear in the stash to have similar remote access is irrelevant (my presumption is that they wouldn’t, because Phylactery Transference will be key to the whole thing working, but if it works for them, great!).

So, short of GM Fiat, how can my floating skull swap between staves?

Will enemies with Wizard spells have spellbooks a PC Wizard can learn from?

I’m aware that Wizards can learn spells from other spellbooks and scrolls they find, as long as they take the time and money to learn it. If there is an enemy, such as a Mage that is listed in the Hoard of the Dragon Queen supplement, that is listed as a caster and said to have Wizard Spells, does this mean we can assume they are a Wizard class and they have to have a spellbook? Is there any chance a PC Wizard could learn the spells off this defeated enemy?

Where are the NPC mages’ spellbooks in the Lost Mine of Phandelver adventure?

In Lost Mine of Phandelver, the party comes across (and presumably defeats) multiple mages. These are not specifically described as Wizards, but their spellcasting is Intelligence-based, and they know spells from the Wizard spell list, so it sounds to me like they are Wizards. (If it quacks like a duck…)

Wizards, in D&D5e, use spellbooks. (See the “Spellbook” sub-section in the description of the Wizard class, p. 114 in the PHB.)

However, the Lost Mine of Phandelver material nowhere mentions the mages’ spellbooks.

Should my party be able to loot spellbooks? Or are these BBEGs actually non-spellbook-carrying casters? Or am I overlooking something?