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
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
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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.
-----------------------------------
Fighter 1 Bard 2
2nd Wind at 1d10+1 per short rest
+1 ac fighting style
17 ac
crossbow
+2 hp
con proficiency
Bard 3
+2 level 2 spell slots
+1 level 1 spell slot
+1 spell known
expertise
+3 skill proficiencies
cutting words
I'd give the bard 3 moderate advantage here.
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Fight 1 Bard 3
2nd Wind at 1d10+1 per short rest
+1 ac fighting style
17 ac
crossbow
+2 hp
con proficiency
Bard 4
stat/feat
I'd give a moderate advantage to the fighter 1 bard 4. (Though there may be 1 or 2 feats that may could equalize that difference)
------------------------------------------------------------
Fighter 1 Bard 4
2nd Wind at 1d10+1 per short rest
+1 ac fighting style
17 ac
crossbow
+2 hp
con proficiency
Bard 5
Level 3 spells
Short rest bardic inspiration
Bard 5 wins big time here.
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So through those 5 levels I'd say the solo class bard is better. It's a somewhat subjective comparison and so you may come away with different results than me but I did try to be fair about it.
I don't think level 6 does anything to change the comparison because bard 6 gets a strong benefit. Level 7 is in the same boat with level 4 spells.
I'm seeing the solo class as significantly better through those levels. At some point probably at level 12 the multiclass variaint will pull ahead for a while IMO.