So,
It makes sense to me that most multiclass combinations should have problems, sort of like randomly throwing ingredients into a pot. Lima beans and jello? Chorizo, spearmint gum and cauliflower? Salt and sugar and nothing else? Most combinations of anything don't work.
It also makes sense to me that there are a few levels at which being a single class really shines. We're talking about level 5 here, in which every exception the OP recognizes (without argument) to his premise that "multi-class sucks" involves the multiclass getting a second attack through some other means: Combos that leverage Eldritch Blast or SCAG melee cantrips or Moon2 bear. But an analysis at level 17 would have a similar problem: What really compares to a 9th level spell (available to half the classes in the game)? At level 20, those moon druid multiclasses no longer look so good! Naked level 20 barbarian with AC24? Etc.
But Fighter1/LoreX is a perfectly reasonable multiclass: It doesn't shine at level 5 compared to a normal Lore Bard, but players who take this route do so to increase their chances of surviving to reach Bard 5 at all. Taking Bard5 first ruins the big benefits: Con proficiency for sustaining spells, Heavy Armor (and maybe HAM) for better defense, probably another +1AC from a defensive style, 2 more hp...
Cleric1/WizardX seems reasonable too: Sure, at level 5 you have nothing that compares to a straight Wizard's level 3 spells. But maybe that's a worthwhile price for not being a squishy, for knowing all Cleric level 1 spells and for having more spells and more cantrips available to cast, and some other Cleric1 benefits.
Fighter1/WizardX? Again, less happy at level 5 but the Fighter level must come before Wiz5, and provides real benefits.
Various weird things, often involving Rogues (eg: get the drop using Assassin, quicken and twin a melee cantrip using Sorcerer, and then action surge to do that again in your first round.... or grab all the skills&cantrips using lots of dips...)
Finally, I think it is completely normal for multiclasses to be better at some levels and worse at others. Even single-classed characters have peaks and troughs that are not always in sync with each other, sometimes to the point of woe: Moon Druids are the poster boys of this kind of feast or famine, but other classes are not utterly immune.
All this said, I think it is reasonable to advise would-be optimizers to think carefully before delaying access to a class' signature or important ability: Is it really advisable to delay a second attack or 3rd level spell? Or to divert from a beeline to Paladin6 and one of the very best abilities in the game? (Getting a few points of dpr for one character feels good, but adding +3 or +4 to everyone's saving throws breaks Bounded Accuracy in your favor!) Sometimes the answer is yes, but that's not the way to bet. Because, you know, chocolate ice cream and high grade motor oil.
Anyway,
Ken
What of the Sorcerer 3/Warlock 2, with as many level 1 and 2 slots as he cares to create, or the Heightened Faerie Fire, or the Quickened Bless, or (I could go on listing metamagic improved support but I wont)?
Odd, I don't remember mentioning Eldritch Blast anywhere...It's a fine multiclass but it uses eldritch blast which was excluded since anything can multiclass with eldritch blast.
So your first 2 paragrpahs were spot on.
The 1 Dip multiclass combos with spell casters are perhaps the least offensive. That's not me saying they are reasonable though.
I'll give you a full right up of levels 1-5 for the first one you mentioned as an example
Fighter 1
2nd Wind at 1d10+1 per short rest
+1 ac fighting style
17 ac
crossbow
12 hp (assuming 14 con)
con proficiency
Bard 1
2x sleep
13 ac
10 hp
bardic inspiration
vicious mockery / crossbow
I'm not into claiming 1 first level class is better than another (except maybe barbarian....)
So level 1 is a tie
------------------------------------
Fighter 1 Bard 1
2nd Wind at 1d10+1 per short rest
+1 ac fighting style
17 ac
crossbow
+2 hp
con proficiency
Bard 2
13 ac
Song of Rest
jack of all trades
+1 level 1 spell slot
+1 spell known
I'd give the fighter 1 bard 1 a slight advantage here.
The fighter's AC is wrong throughout. AC is 19, not 17. Chain mail, shield, and defense style = AC 19. That gives us:
Fighter 1 Bard 4
+3d10+3 (18) HP from Second Wind
+6 AC
crossbow, net proficiency
+2 hp
con proficiency
Bard 5
Level 3 spells: Fear or Hypnotic Pattern 2/day
+8 Bardic Inspiration die
wis proficiency
The fighter/bard has about twice as many effective HP (54-59 HP counting Second Wind vs. 33-38 HP) and +6 to AC. The fighter/bard is much, much better at physical control because leveraging physical control relies primarily on your AC and Athletics. (He may e.g. cast Heroism on himself for temp HP and then wade into melee, grappling with his Athletics Expertise and then shoving bad guys prone on the followup round, which essentially takes them out of the combat.) He can also afford to get close enough to toss nets on enemies. The pure bard behaves more like a mage: he has to stay off the front lines, and he's got one or two big guns per day to deploy--but one of his best spells, Fear, requires him to get close to the front lines. (It's a 30' cone originating from the caster.) He gets it earlier than the Fighter/Bard, but he can't use it as well, so it's really only like getting it half-early.
So the fighter/bard winds up playing kind of like a tanky fighter/mage, and the bard ends up playing more like a squishy cleric. It's certainly not obvious to me which one is "better." They seem comparable.
So? You were comparing class not characters. That the MC Bard can be a melee character is a point for the MC, not one of dismissal (which you sure seem to be doing a lot of).Mine were using crossbows so ranged weapons didn't start to favor the bard. There's no way a bard 1 ever should go into melee. So yes you can mention 19 ac but then you are comparing a melee character to a ranged character.
So? You were comparing class not characters. That the MC Bard can be a melee character is a point for the MC, not one of dismissal (which you sure seem to be doing a lot of).

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.