The "tenth" plague was actually announced at the very beginning Shmos 4:23
So I say to you, 'Send out My son so that he will worship Me, but if
you refuse to send him out, behold, I am going to slay your firstborn
Send out My son… but if you refuse to send him out, behold, I am going to slay, etc.: That is the last plague, but He warned him
[Pharaoh] about it first, because it was [the most] severe, and that
is what [Scripture] says: “Behold, God deals loftily in His power”
(Job 36:22). Therefore, “who is a teacher like Him?” [A man of] flesh
and blood who seeks to avenge himself against his fellow, concealing
his plans, so that he will not seek rescue, but the Holy One, blessed
be He, deals loftily with His strength, and no one is able to escape
from his hand, except by returning to Him [by repenting]. Therefore,
He teaches him [about possible punishment] and warns him to repent. —
[from Tanchuma, Va’era 14, Exodus Rabbah 9:9]
Now that Par'o has refused to accept the warnings and the punishments of the other plagues, and has told Moshe that he will refuse to see him or accept any warnings
Pharaoh said to him, "Go away from me! Beware! You shall no longer see
my face, for on the day that you see my face, you shall die!"
[Thereupon,] Moses said, "You have spoken correctly; I shall no longer
see your face."
then he has made himself subject to the original punishment. He has been given the last chance and he has turned it down. Once he has refused the last chance, there is nothing more to be said. Otherwise, you can ask why 10, why not 20 or 30, ...
Bo chapter 11 shows how Moshe responded to Par'o and said what was going to happen as a result. This was not a "warning" but a statement before he turned and walked out.