The Dragon alone spits out 45 odd damage with its breath weapon on an average damage roll in an AoE. One lucky breath weapon roll or two and its likely game over for several PCs.
Ok so I decided to take your bait after thinking of it. We will compare a single class 5th level Enchatment Wizard vs a 3rd level Enchangment Wizard/2nd level twilight cleric. The party is 4: this character a Melee martial, a ranged Martial and a Rougue.
We will use a PHB half elf Elf 5th level Enchanter vs a PHB half Elf 3/2 Enchanter/Twilight Cleric
S15/D10/C12/I16 (18)/W14/Ch10
Both start as Wizard
Comparing these two.
Both Characters have hypnotic Gaze
Both characters have the exact same number of spell slots: 4 1st, 3 2nd, 2 3rd
Wizard advantages over multiclass
+1 save due to ASI
2 3rd level spells teh cleric does not have - we will use the two you mentioned Hypnotic Pattern and Fireball
3 more wizard spells prepared (two are the 3rd level spells above, the third is mage armor)
Can get back a 3rd level slot with Arcane Recovery
multiclass Advantage over Wizard:
AC18 with no spell slot used vs AC13 using a spell slot for the wizard
2 more hps
Twilight Sanctuary
Turn Undead
6 1st level 1st level cleric spells prepared
Advantatage on initiative
300 foot darkvision
can give 300 foot darkvision to 2 allies for an hour
can get back a slot using harness divine power
Spells prepared (
wizard only in red,
multiclass only in green, spells they both have in blac)
Shield, Absorb Elements, Silvery Barbs, Cause Fear,
Mage Armor,
Sanctuary, Healing Word, Bless, PEG, Faerie Fire, Sleep
Web, Vortex Warp
Fireball, Hypnotic Pattern
Let's tale through the fights you mention. We will assume short rest after fight 2 and after fight 4. We will assume bright lighting in every fight so the party with the multiclass does not surprise everyone with vastly superior vision.
Like I mention earlier they have the same number of spell slots so lets start:
Before the day begins the single class character casts mage armor
1. Hobgoblins and Boss = the play here is web. If the 5th level wizard had fear that would be the spell to use, but he doesn't and web is going to generally going to be the best option. Fireball would work if he won initiative (beating all 6 hobgoblins), but if he didn't this is probably not a good time to use it and it is overkill on 4 CR1/2 and a CR3. Upcast cause fear at 3rd level is probably the second best option if you are way down on the initiative order and the enemy is mixed up with you.
We are going to say they both use web
Verdict - tie. The single class has a better save, but the multiclass has advantage on initiative and therefore is more likely to get it off before enemies.
2. Ettins - Ettins have no ranged attack. The play here is upcast cause fear, if one is lucky enough to save you hit him with silvery barbs. They can't advance frightened so all they can do is dodge. You pummel them with ranged weapons, anc cantrips and the Rogue either kites (if he is a swashbuckler) or uses steady aim. If the melee guy feels left out he can kite too. They get an AOO on melee man but it is one attack (with disadvantage) instead of two. They save again at the end of their turn. If one of them makes it you cast the spell again targeting both.
Verdict - They used the same spell but I am giving a slight nod to the
multiclass due to advantage on initiative. If you win initiative you make is so they will likely never get an attack action.
SHORT REST
Going into short rest - They both used 2 second level slots, the wizard also used a first level slot for Mage Armor. I am going to say both of them used two more 1st level slots on shield or silvery barbs. This is being generous considering the multiclass has the same AC without shield as the wizard has with it.
Wizard uses Arcane recovery gets back 1 1st, 1 2nd. Cleric uses Harness Divine Power getting back 1 1st and arcane recovery getting back 1 2nd
At the end of this rest they have the following in slots:
Wizard: 2 1st, 2 2nd, 2 3rd
Cleric: 3 1st, 2 2nd, 2 3rd
3. 4 Gargoyles: This is where it gets interesting. Initiative order matters a lot here.
Hypnotic Patter will probably make them all lose a turn and probably one of them will lose 2 turns. That is a good play if you win initiative. Fireball is good if you win initiative too. Problem is you need to get all of them for those to be really effective. The chance the single class Wizard will beat all 4 in initiative is 17%. If he had a 16 dexterity instead of a 10 it is still only 32%.
The chance the multiclass character will win initiative is only 29% but he does not have these spells anyway. he does have Faerie Fire, which is probably what you want to do if you win, but even with advantage he does not win most of the time.
That means if you go to your AOE you are left with using an AOE that probably only hits 2 of them, fragging allies, or using a spell that you can target only a few individuals.
Of note Gargoyles also have no ranged attacks meaning something that keeps them away is ideal
Given that I think upcast cause fear at 3rd level on three of them is the best play for both players here. You probably don't get it off before a couple of them swarm you, but you prioritize ones that are not yet engaged and if you hit some that are engaged either they have disadvantage or your allies can disengage. Bless would be an alternative for the multiclass character, probably upcast at 2nd level, but unless you are at the very bottom of the initiative order I think upcast cause feat is better here.
Verdict - I am actually going to give slight not to the
Wizard because of the higher save DC. Initiative would be important if the multiclass had the 3rd level spells but he doesn't
4. 1 Ghast and 4 Ghouls
The Wizard probably uses web here, even if he only catches a few. That is a good play. He could fireball, but he has a long day ahead still. The multiclass can turn undead though and that takes on average 3 of them out of the fight completely.
Verdict - Cleric
We are going to say each of them used another 2 1st level slots on either shield or absorb elements
Short Rest:
Coming out of this short rest:
Wizard slots: 0 1st, 1 2nd, 1 3rd
Multiclass slots: 1 1st, 2 2nd, 1 3rd
5. 2 Wyrmlings:
There are a lot of options here and it depends on if this is outside or inside. We will assume it is outside and the wyrmlings will use flyby tactics when out of breath. By saying that I mean they will fly over everyone come down and attack someone with a ranged weapon (or no weapon) and climb back up to range.
I don't think you use a spell here, especially if you know momma is around.
Verdict - tie
6. Young Black Dragon
You gave this dragon legendaries, which means save or suck is useless and the party does not have enough spell slots to burn through his legendaries.
going into this the multiclass is going to use twilight sanctuary the 1st turn and most likely save slots (1 1st, 1 2nd, 1 3rd) for either absorb elements or healing word. After the dragon uses a breath weapon he can consider sanctuary as a bonus action cast. Sanctuary has the potential to actually burn through more than one legendary because he saves every time he attack the multiclass. This might work it might not, if he gets down to 0 and he has no legendaries lefe, cause fear is an option which would mean if he is using a flyby attack that he can't attack until he saves)
The Wizard is going to open with Fireball, but it is not going to be nearly enough.
Verdict cleric by a lot- Twilight sanctuary cancels dragon fear and if the character does not have dragonfear it gives him hps.
So there you have it - 6 fights, the single class uses more slots and still does a lot worse in 2 of the engagements