Monster (Lich et al) Stat Blocks

Why do Lich's and other equivalent monsters that have their origins in being a being similar to a player character (presumably a wizard) not have spell casting abilities that resemble such.  I would have thought that a Lich would have spell casting abilities that resemble a wizards (with possible enhancements) in terms of spells, flexibility and the ability to learn more rather than the limited forms of spell casting that we are presented with.  Otherwise, why become a Lich?

Monster stat blocks are designed for a fight. A single fight at that. Once the initiative starts, the monster’s life expectancy drops to less than 1 minute. As such, the stat blocks are made to show an effective load out for that CR creature. The designers tend to cut out the utility spells they might have ready, but won’t come up in a fight. Like, a lich who can scry makes tons of sense, but a lich who cast scry in battle would be very unusual. So they leave it out so as not to clutter the stat blocks.

If you as the DM want to give a lich a pack of other spells, have at it. It really makes sense that they might have a bunch of other spells prepped. 

Most tier 4 fights are usually underwhelming because when you get there, each member of the party is a walking Christmas tree of magic items raiding the Lich's tomb like a kindergarten class on an Easter Egg hunt and treating your Lich like 50k XP loot-piñata. Most DMs I know that are used to tier 4 play (including myself) redesign and homebrew tier 4 monsters to be an actual challenge to a tier 4 party (and also its helps against metagamers).

They used to in the initial 5e, but it got cut back to the current model for new monsters a year or two before 5.5 dropped. Honestly, I think it's a weak change, since it generally ruins players' ability to gain useful information from observing the creature cast utility spells and several blocks that ostensibly are for powerful spellcaster creatures now have a repertoire of maybe 6 spells. It's not awful, but it's a major blow to the verisimilitude element of spellcaster NPCs.

If you're referring to the 2024 Lich, it's purely for simplicity and removing bloat for combat. The 2014 statblock included spell slots, all their prepared spells (wether they're combat spells, utility spells, or wether they can even be usable in combat) on their starblock, which is good for giving ideas what a lich can use before a fight, but ultimately was clutter taken up when the lich was in combat (which is where statblocks are primarily used for).

As Xalthu said, you can easily add in and switch out what spells you want, and what utility spells it has access to.

(I personally shadow tack on the 2014 spell list for utility and some other spells).

The 2024 stat blocks are designed to be easy to use and hit CR targets, not for verisimilitude; the 2014 lich has a whole bunch of spells and spell slots on its stat block that it's unlikely to use in an actual encounter, so the main effect of them being there is to add pointless work for the game master.

It's a reasonable choice when the only purpose of a monster is a one and done fight. It's less reasonable when a monster is supposed to be a behind the scenes enemy for man sessions and "what can this BBEG actually do" is something the game master wants to think about, but to be fair, it's not actually something the 2014 stat block did well either, because what it really means is you should list the primarily out of combat spells the BBEG has access to and might choose to use.