1 ticket for 10 apples worth it?

Honestly, the ticket and the mats that you might miss out on from this or any other exhibition matches is not going to impact you long-term. These fights are just there for a challenge, but are not meant to punish players who can't do them.
That being said, see if you can find a a friend with a leveled Amakusa (Ruler). That servant with some heals and buffs can probably power you through this fight without even needing Medea or some other buff remover.
As for apples, you're not using them to complete exhibition matches, but to power up your roster since now is your best chance.

Idk how much you have been rolling the lottery, but this event is one of the best opportunities to level up servants thanks to the "infinite" supply of XP cards thanks to the roulette. You won't be leveling those servants for just a ticket, but you'll be enhancing your rooster for future challenges. So don't see it as a trade of 10 apples for 1 ticket, but a trade of 10 apple for a two max ascended servants. So my answer es yes, burn those apples.

Just dont think about the ticket and just realize the potential of this event. Nero fest really has a lucrative amount of mats and exp cards that it should at least max level any of your servants(add in the QP as well). Getting my servants to max level is always a good trade off for a measly ticket that wont even guarantee you a servant. In conclusion : Burn as much apples as you want while event lasts.

What other Servants do you have access to? In general, there are good gameplay reasons to invest in Nursery Rhyme, but if you absolutely don't want to spend a lot of EXP on her, I think you can beat the event without her. My team was level 60 NP5 Medea (make sure you max ascend her and do her strengthening quest to get her third skill), level 65 NP5 Hans, and a support Tamamo; Hans died, but only at the end of the quest, at which point Mash switched in. So, if you have your own Hans, access to a good support Tamamo, and level up Medea, you should be able to beat the quest with a budget-friendly team.

Nursery Rhyme, or any aoe casters is no need at all. Medea yes, she fields you with excellent ST NP whilst removing that annoying debuff

i did it with Waver/Medea/Caster Tama as support (no one dies, so no point in mention backup), but if u dont have Waver i suppose Hans will work

There's really no need to max out any servants for this. Medea only needs to be high enough level that she doesn't die. Just getting her to like level 40-50 should be perfectly fine, since she takes half damage from all the enemies in this quest. You don't really need her damage... You just need her to remove the buff from the boss assassins before you kill them. In fact, if you already have someone else already leveled, who is capable of removing buffs, you can even use them instead. I used Jack the Ripper instead. Medea is just what was recommended since she is a caster, so she will take less damage from the Assassins, and her multiple arts cards play nicely with the other casters that you'll probably use for this.

You don't really need to use your own Nursery Rhyme at all. Anyone who can do nice damage is fine. A caster is not necessary, but is recommended because they have class advantage. The main damage dealer will be the one landing all of the killing blows, so they will be eating all of the defense debuffs, so it's helpful for that servant to be a caster since they take half damage from the assassins. Just use Hans, plus a level 40-50ish Medea, plus one borrowed AOE caster DPS, and you'll be golden.

Or even just borrow Amakusa Shirou, and pair him with Hans + one other support, and you don't have to worry about buff removal at all.

But as far as your base question goes (about whether or not one ticket is worth 10 apples), you can't really answer that question until after you use the ticket. One ticket is a potential SSR, but it's also a potential Spicy Mapo Tofu. If you get a really nice SSR with that ticket, then it was probably worth 10 apples. If you get a Boudica with that ticket, then absolutely not. In general, I probably wouldn't invest heavily in a servant that I honestly thought that I would only use for this one quest, and never again. But there are probably very few servants like that.

You can always borrow an AoE caster, if clearing Hassans en masse is your problem. Caster Liz, Nursery, Babbage, Geronimo are fine. For buff removal, Medea or Diarmuid can be used however, Medea is easier to Arts chains in and can instantly give you an NP on demand.

Or you can ultimately find a super buffed Medea that can nuke the suicidal Hassans from a single NP but FinoPlays (a youtuber) said that Medea instantly killing those Hassans will still trigger their passive. I'm not sure if that's true or not, or changed for our event (if it was a bug on JP) but try giving it a go. Medea then would need proper heal support, someone like Iri or Medea Lily.

Ultimately, i have someone with a level 100 10/10/10 Amakusa with MLB'd White Rose. His NP cleanses buffs as well and he's a Ruler so that eliminates the possibility of having to have a buff cleansing Caster + AoE Caster for wave clears. He can do both.