Undertaker's sexual identity?

My main reason for not thinking of Undertaker as asexual is because it's very important to my theories that he fathers Vincent and Francis/Frances with grandma Phantomhive. And I doubt he'd have sex with her (or anyone) without wanting to. Forcing himself to have kids with a human just for the point of pissing off the royal family doesn't seem like a strong enough argument.

I guess you could say he's sex-favorable -- how is this considered asexual? -- and just passively accepts an offer from her, but I don't see him that way.

Plot device to delay the inevitable

That's basically what it is... that when they first make their contract, our earl decides that instead of searching out whoever attacked the Phantomhives, he's going to let them come after him in an attempt to finish the job.

He assumes that all the assassins sent to kill him on a somewhat regular basis are just pawns. He's waiting for the person or persons who ordered the attack(s) to show themself/selves.

Apparently, he and Sebastian realize it's not someone like Haku, either. Because he's out of the picture, replaced by Lau. And they don't seem to suspect Lau, since he's been so useful and helpful. Lau has made asides to himself (or perhaps they were just thoughts) that are very suspicious, but I don't think he could even possibly be the "big bad" here. He wouldn't be behind the original attack, anyway, all the way from China, before he had much power. He was already sending letters back and forth with our earl before leaving China, and it could simply be that our earl was planning to get Lau to England and in charge of the local branch of Qīng Bāng... specifically because Haku needed to be "dealt with". Our earl was trying to put together a loyal network of evil nobles and route out the disloyal members of the extended network, too -- like Haku and Vanel.

His father's network seems to have included some very disloyal members. I believe at least two of them were high-ranking members of the cult that bought the twins. And then Kelvin was in the extended network.

Personally, I think Sebastian has at least an idea about who the true culprits are -- the one who ordered it, at least -- and maybe even someone who was involved in her decision making process. Just like Sebastian figured out, before our earl did, that Jack the Ripper was likely Madam Red and Grelle working together, he might have already figured out the ones who plotted the attack were probably Queen Victoria and John Brown. With John prodding her to it, and then her ordering it. He wants his young master to figure out who Jack the Ripper is. Similarly, he might be waiting for our earl to put the pieces together about the "doting" queen and her odd master of horses... with that damned Prince Albert puppet of his.

Our earl suspects his own aunt Angelina of being Jack the Ripper, but it is some final timing clue presented by Sebastian that tips him off it has to be her and Grelle. Something should finally tip him off about the queen and John. Who knows?

Maybe he finally realizes the puppet serves John in a way that something similar would have served Sebastian... if our earl had agreed to the original offer for the demon to make him think his twin had returned. I wonder who might comment about the puppet and get our earl to thinking about it. 🤷🏻‍♀️

Or -- and this is more likely -- our earl thinks about the timeline and circumstances of the Tower Bridge project... and finally realizes how much the queen has gained from having control over the Phantomhive estate, coffers, and entire earldom for a few months. She would do anything for her "Prince Albert", and that bridge is historically dedicated to his memory.

Marriage arrangements

There possibly would have been an arranged marriage for both, but since our earl wasn't expected to inherit, there wouldn't be as much expectation for him to marry. If they'd had a daughter, there would have been more pressure to marry her off. They might have arranged a marriage between their daughter and Edward.

If Madam Red had borne a daughter, as she'd hoped, that daughter could have ended up betrothed to our earl, even though there would be a nearly ten year age gap. But I'm sure they could find someone much closer to our earl's age to match him with, if they wanted to arrange a marriage for him. The only thing is, the way Madam Red obsesses over Vincent, she might plead for them to have our earl wait until her own daughter was old enough to marry him.

Lizzie was meant to marry real Ciel, since he's the older twin, the original heir intended to become earl and watchdog.

She treated (and treats, technically) real Ciel as her betrothed. Our earl, she treats more like a brother or friend. Of course, right now she's angry with our earl and also angry with herself for not being able to tell them apart when our earl was pretending to be real Ciel.

This weird arrangement of marriages between cousins reminds me of the comparison I did between Black Butler and the Egyptian myth about Thoth helping the goddess Nut bear her five children: Osiris, Set/Seth, Horus (the elder), Isis, and Nepthys -- the siblings intermarry and have affairs, leading to Set/Seth killing Osiris, Isis getting Osiris resurrected, etc. Except here, we have Rachel giving us real Ciel (Osiris) and our earl (Set/Seth), Francis/Frances giving us Edward (Horus the elder) and Lizzie (Isis), and Madam Red was trying to have a daughter (Nephthys). Let's not forget that mysterious Osiris group mentioned by Rian Stoker. That might be how Undertaker was introduced by Druitt to Stoker in the first place....