Esther was the creator of the Vampirism Spell. This means she could remove literally any facet of the spell she didn’t want or add new properties to the spell, like she did with Alaric. Now, Esther’s main goal for coming back to life was to create an Original Vampire that would wipe out all her children, with an indestructible stake (which she knew would also wipe out all their turned progeny).
With the above factors in mind, there is no logic in thinking that she’d allow the Sirelink Spell to go into or be part of Alaric’s creation. That would be counter productive.
She’d also know that even if Alaric would never turn anyone on purpose because of his hate for vampire (similar to how Mikael never ever turned anyone because of his self-hate) his blood could be stolen and used to make one vampire that could go on to create 000s of vampire in literally a day and on and on and on. Bringing her back to square one.
These canon reasons leads me to believe she didn’t include the Sirelink Spell when making him, or she edited it out of the composition of the Vampirism Spell. She’s its creator.
The only way I ever see her allowing Alaric the ability to sire new vampires is if she also made it that any vampire he sires would also inherit his hatred for vampires and (like Mikael) only feast on vampire blood (or starve to death). That way, Alaric would be creating “anti-bodies” (his sireline) that go after “infections” (other vampires), wiping them off the face of the earth and when he dies, they’d all die with him. This would make his work (and Esther’s goal) much easier to achieve.
It wouldn’t make any kind of sense whatsoever that Esther would allow him the ability to sire new vampires, if they’re just gonna act like every other vampire. The average vampire is a destructive force that takes the lives of countless innocents and spread so quickly that the death toll is multiplied. As a teenager, Elena would technically have 80-90 years tops, before old age comes and takes her. That’s nearly a century of Alaric-generated vampires wreaking havoc on the earth. That doesn’t seem like a mistake Esther would make again, especially since she’s the creator of the spell who could just edit that bit out of it since it literally doesn’t serve any single purpose to her course.
She was a magical genius. She wouldn’t be that sloppy after 1000 years of learning from her mistakes in creating vampires.
Instead of all the drama of having to deal with a new sireline, just remove the ability to create them. Problem solved. He can then have laser focus on his assignment and not worried about someone stealing his blood, while also thinking about protecting Elena from untimely death.