Nice analysis. But way off in what was really happening at tables. Synergies has to be taken into account. The cleric was more or less a healbot and its true fighting capacity came at third level with silence and hold person spells.
I beg to differ. I played and ran D&D and AD&D for 25 years, 1000's and 1000's of hours. The supposed 'synergies' are overrated on the whole. Clerics as healbots changes nothing either, I am assuming in my assessment you would be insane to vary from 4x CLW at level 1, period. MAYBE, you might sub in a Bless or Protection From Evil if you have specific reasons. I suppose any of the other level 1 spells might also be useful if you can anticipate the specific use (IE going in with a specific plan). All that does is increase their utility. As healers a level 1 cleric represents a spare 4.5x4 = 18 hit points, roughly doubling the melee endurance of the ENTIRE party (assuming a 5 PC party). Their fighting capacity is better than 80% of a fighter at level 1 (they are exactly 1 hit point shy of being a fighter, though they probably do a bit less damage, maybe the fighter gets a STR bonus to-hit, etc.). And yes, 3rd level, where they get all their 2nd level spells, including bonus spells for WIS, is a BIG power increase.
Think about it this way though. You would virtually ALWAYS be better off building a party with clerics subbed in for fighters. Yes, damage output will go down slightly, but not much, and total party hit point endurance, plus general spell casting, will improve greatly. Fighters are pretty good at lower levels, but nothing like vital. Clerics are vital. To the point that dropping in a half-elf that has a cleric 2nd class at party creation is practically a standard optimization tactic! (making the thief a MC'd thief/M.U. being another, elves are better thieves anyway).
The wizard might get double its spell allotment but there were usually more than one fight per day and fights were resolved way faster back then. This left your wizard stuck with darts and daggers for most fights. The wizards' job was to know when to cast their spells to tip the balance of hard/ key fights.
Right, and those are the ones that are high risk where you have to have that added power to win. Again, this is why standard optimization tactics for a 1e party is to sub in elf fighter/M.U., or clerics, or HE cleric/MU, etc. to get the extra spell power is so excellent a strategy. (at least at low levels) having all Magic Users won't work, but you could easily go half-and-half clerics and Magic Users, that is pretty optimum, particularly if one of the Magic Users is also a fighter, so 2 clerics, 2 magic users, and a magic user/fighter MC. Lots of spell power, plenty of melee when you need it. Remember, melee is a failure condition in 1e anyway, so what you need is the ability to survive that mistake now and then.
This is also true with the thief. A backstab was a relative rare occurrence at low level. Most of thieves' job was to find/remove trap and to scout ahead. They were not the damage dealer they are today.
No, but if they cannot deal damage effectively, they are greatly reduced in value. Also, certainly at low levels, thieves are terrible scouts! Their thief ability check numbers are rotten, unless they are elves, who can already sneak better than any thief! So why not be an elf magic user? Or even elf magic user/thief? See my point? Now you begin to understand why elves were made to be less desirable by level caps!
Also, no classes were guaranteed average HP from the get go. I have seen fighters with 18 con having a mere 40 hp at level 6 and a wizard of level 11 with barely 21 hp at 11th level... Your first level cleric might only get one additional HP for its second level. This is hardly doubling hp. Average hp on leveling was not thing in AD&D. At least not at every tables. I have seen players use a wish to reroll a bad HP roll that they had.
Yes, but I have no idea how that effects considerations of class design, which cannot really be based on what might happen in some specific case. Obviously you could have a 4th level fighter with 4 hit points. I've seen stuff like that, it is pretty sad. It isn't a reflection of the class though, particularly. Though I must say that a 4th level MU with 4 hit points will grumble and be in some extra danger, but it isn't going to cripple him...
Also, you also have to remember that a wizard was not a true wizard until he reached name level and so was it with all other classes. You were simply dabbles in your class until you reached that name level. When my players were meeting a paladin, they knew immediately that the NPC was 9th level. If it was Justicar, it was an 8th level paladin in becoming.
Again, I am not sure how this is relevant to the discussion at hand. Level titles have no mechanics associated with them, and I'm not sure why they would matter in terms of how the XP tables are organized.
This is why training was a thing. Yes it was a mean to relieve players of their gold, sure. But it also reflected the journey that they had started. They needed time to assimilated what they had learned and training was also to make them learn more about their profession. Contrary to modern RPG and 5ed, the starting characters were simply apprentices, novitiates in field. They were not fully formed and ready. I consider the AD&D characters as people that have learned the basic of their trade. Started to work/adventuring before fully ready and taking time to learn more about their trade in their downtime, taking time to catch up with what they have missed by going away early in their training...
Sure, but that still leaves the question whether that made the game fun or not. Nobody can answer that for anyone else. I always thought the whole training thing was an interesting idea, but not well-thought-through nor especially appealing. I guess most people agreed.