I'm pretty strict on the horns being kings and not kingdoms for 2 main reasons:
1.) because scripture doesn't state the saints would inherit the kingdom after around 15 kingdoms (Babylon, Persia, Greece, Rome, 10 horn kingdoms, 1 little horn kingdom). It states there would be 4 kingdoms but the saints would inherit the kingdom forever (Daniel 7:17-18).
2.) because scripture states out of the 4th kingdom (malku) 10 kings (melek) would arise. It doesn't state 10 kingdoms (malku) would arise out of 10 kingdoms (malku) (daniel 7:24)
I'm not so sure if the early Church father's expected 10 kingDOMS after the roman empire.
1.) Jerome doesn't appear to believe there would be 10 new kingdoms after the Roman empire, but that when the Roman empire is to be destroyed, it would be partitioned between 10 kings. I read this to mean that just prior to the 4th kingdom being destroyed, it would be partitioned between 10 kings, followed by an 11th that would pluck up 3 of the 10 kings. This is would be consistent with vision in which the 4th beast is slain (rome destroyed) when the little horn is judged. He states this was the tradition of the Christian church. This doesn't appear to be the traditional historicist/futurist belief. Additionally, this interpretation is proved false by History. For Rome never had 10 kings rule over it followed by an 11th king to overthrow 3 of them just prior to its destruction.
"We should therefore concur with the traditional interpretation of all the commentators of the Christian Church, that at the end of the world, when the Roman Empire is to be destroyed, there shall be ten kings who will partition the Roman world amongst themselves. Then an insignificant eleventh king will arise, who will overcome three of the ten kings... after they have been slain, the seven other kings also will bow their necks to the victor." (Jerome 347-420 AD)
2.) Cyril of Jerusalem seems to believe the same thing as jerome, that prior to Rome's destruction, it would be partitioned and ruled over by 10 kings, and after these and 11th king would rise. He states this is also in tradition of the Church's belief. This doesn't appear to be the traditional historicist or futurist belief. Additionally, this interpretation is proved false as the Roman empire never had 10 kings rule over it at the same time, followed by an 11th king just prior to its destruction.
The fourth beast shall be a fourth kingdom upon earth, which shall surpass all kingdoms. And that this kingdom is that of the Romans, has been the tradition of the Church’s interpreters ... There shall rise up together ten kings of the Romans, reigning in different parts , but all about the same time; and after these an eleventh, the Antichrist, who by his magical craft shall seize upon the Roman power; and of the kings who reigned before him, three he shall humble, and the remaining seven he shall keep in subjection to himself …(Cyril of Jerusalem 313–386 AD)
3.) Tertullian seems to believe similar to what the Historicist traditionally believes, that the Roman state would be transformed into 10 new kingdoms.
For the mystery of lawlessness is already at work, but only until the one who now restrains it is removed. What obstacles are there but the Roman state, the rebellion of which, by being scattered into the ten kingDOMS, will introduce the Antichrist upon its own ruins?(Tertullian 160–220 AD)
4.) It's hard to tell if Hippolytus believed the 10 kings would start new kingdoms after the Roman empire or if it would be 10 kings who ruled the Roman empire.
“A fourth beast, dreadful and terrible; it had iron teeth and claws of brass.” And who are these but the Romans? - the kingdom which is now established ... After this, what remains, but the toes of the feet of the image, in which part is iron and part clay, mixed together? And mystically by the toes of the feet he meant the kings who are to arise from among them. (Hippolytus (170–235 AD)
5.) It appears Irenaeus also holds that the Roman empire would be partitioned and ruled by 10 kings. However, it's hard to see if Irenaeus believed these would be 10 new kingdoms AFTER the roman empire or if the Roman empire remained, but just ruled by 10 kings. If it is the latter, then it was proved incorrect by history.
In a still clearer light has John, in the Apocalypse, indicated to the Lord’s disciples ... concerning the ten kings who shall then arise, among whom the empire which now rules the earth shall be partitioned. He teaches us what the ten horns shall be which were seen by Daniel.(Irenaeus 130–202 AD).
As an Amil-Historicist, you believe it is 4 kingdoms from the time of Daniel (Babylon, Persia, Greece, Rome) until the coming of the kingdom of God, at Christ's 1st coming. But then, the saints would possess the kingdom after around 15 kingdoms (Babylon, Persia, Greece, Rome, 10 horn kingdoms, and little horn kingdom that uproots 3 of the 10 horns), at the 2nd coming of Christ?
It is easy for parabolic language to distract us from the simple interpretation. I would argue, The interpretation of the 10 horns should be shaped on the simple interpretation of the vision: That there would FOUR kingdoms but the saints would inherit the kingdom.
Daniel 7:17-18 These four great beasts are four kingdoms who will arise from the earth. But the saints of the Most High will receive the kingdom and possess it forever—yes, forever and ever.’
Thus, while I don't assign specific names to the 10 kingdoms, as such would only be speculation, I believe these verses (daniel 7:17-18, Daniel 7:27) already fulfilled, in that the saints inherited the kingdom around the time the 4th kingdom, which would be consistent with the NT.
Luke 21:31-32 So also, when you see these things happening, know that the kingdom of God is near. Truly I tell you, this generation will not pass away until all these things have happened.