I do not believe spell blocks belong in a stat block unless they are a custom spell.
CR2 mages generally have something like 7 spells. CR 4 wizards can have 10, and CR6 wizards can have 14 or more. Even at 6 point font, which is not very readable, the spellblocks can take several pages. Some spells on their own can take most of a page. Placing that in the book would break up the context of what was going on, and doing that for every wizard would cut down on story content considerably.
1. Most spells can be summarized in less than a line. A couple may take 2 or may be too complex to summarize. Your CR 4 wizard will take maybe 12 lines, and your CR6 wizard might take 16. Unless you are statting out an entire wizard's guild it won't take "several pages." Even if you were statting out an entire wizard's guild, the spells will overlap and it won't take "several pages."
2. How exactly would it cut down on story content? They are two separate things. Unless you are assuming these things are written with a word count limit of some sort, in which case, where are you getting that?
3. The vitals of a spell don't really need to take more than a line. The DM doesn't need the fluff. For quick operation the DM only needs a couple of stats such as range, area, damage, and saving throw.
As for why weapons are included in a stat block and spells are not: Most creatures have 0-2 weapons from the weapons table. Spellcasters generally have lots of spells. Weapons are generally very simple, follow the same pattern, use different ability modifiers for different weapons, and sometimes have special abilities. These short blocks that change for every character. Spell blocks are longer, never change and can be consolidated in one location. The parts that do change, the attack bonus and DC are placed in the spellcaster's stat block, but they are the same for every spell the spellcaster uses.
I'm not sure what you are arguing here. You are saying that weapons are simple but then you argued they have special abilities and are therefore not simple. Also, spell blocks DO change more than weapon blocks do. Attack spells alone have two types of attack mechanisms, up to 6 types of saving throws, and several different types of durations, actions, targeting effects and scaling mechanics, and this is without going into fluff like components. The DM can guess what a weapon does pretty handily without a lot of help, if you are unfamiliar with a particular spell you HAVE to stop play and go look it up. That is more reason why a quick-read line spell line for creatures would be helpful.
The next paragraph is not to criticize how you write spell blocks but to point out how difficult it is to concisely describe a spell in a line or two.
I don't feel the spell blocks, as you have written them here, are very readable. The abbreviations make things difficult to read and do not convey information clearly. The only thing that is abbreviated in stat blocks at the moment is saving throws. The abbreviated spell blocks also have information that is wrong and missing. The 1d20+0 does not really seem to mean anything. It is next to the damage type, but you do not roll a d20 for damage, and the attack roll is not 1d20 + 0. It includes the full bonus for an attack. Shocking grasp's attack roll is d20 + spellcasting ability modifier + proficiency. It does not use dex. The summarized spell block also does not mention that the target cannot take reactions after a hit until the start of its next turn.
That just means that the summary he proposed needs improvement. You just need to have a standardized system of notation like shorthand, and you place key of the abbreviations somewhere in the PHB. After that is easy. Most spells take less than a line. Shocking grasp has a couple of non-standard things so it wraps onto a second line. For some spells like Prismatic Spray, you may just have to say "see PHB p.XX" after special if the special effects are longer than a second line. Most of the spells which you can't easily summarize are non-combat spells though. They don't need to be summarized in a combat stat block.
Fireball: L3; CT:1A; R: 150'; AoE: 30' radius sphere; Save: Dex 1/2; Dam: 8d6 Fire; Scale: +1d6/lvl; Special: none.
Shocking Grasp: L0; CT: 1A; R: Touch-Attack; Save: No; Dam: 1d8 lightning; Scale: +1d8 5th, 11th, 17th lvl; Special: Advantage to attack if target wears metal; target hit can't take reactions until start of next turn.
If you want the stat blocks, copy and paste the spells onto a page and insert it into the book. It looks like most spells in WotC's adventures will be available in basic pdfs or supplements. Or get the spell cards. By providing your own spell block page information, you have exactly the information you want, and it does not impact everyone else with extra pages of text in large breaks in the story, added cost or reduced content.
1. Again, where are you getting that a couple of extra lines increases cost to the consumer or reduces content? If they improve the players' ability to use the product I don't think WotC would object to adding a few more lines. They wasted enough text in the spell description section of the PHB that it is pretty clear they aren't that concerned about word or page counts.
2. If Hoard of the Dragon Queen is any indication, monster stat blocks come in the appendix, not in the story. There is no reason that would affect the flow of the story in any way.
3. By your reasoning there is no reason to put the monster stat blocks in any adventure either. They would also break up the story, add cost and reduce content. You can also just look them up on the monster manual just as easily as you can look the spell up.
