To quote HBO’s Rome, “if my last coin buys me a throne, it will have been worth it.”
Yes, potentially I might have to deal with an Essosi alliance down the line. But the Triarchy lasted 34 years on its own, so it’s not like I don’t have time.
And since what I’m actually after is Westeros, losing the Three Daughters after I take Westeros is an acceptable loss, but I could potentially buy off my opponents by giving them Myr and/or Lys and still be in the positive.
Then again, if and when I’ve taken Westeros, I’ll have a lot more resources to hold onto the Three Daughters if I want to.