Using your own philosophy again... reveals how historically inaccurate and un-Biblical your theory is.
Have you ever considered why... Apostle Paul said he was born of the tribe of Benjamin, and also claimed to be a JEW? (Romans 11:1; Acts 22:3).
1 Kings 12:19-21
19 So Israel rebelled against the house of David unto this day.
20 And it came to pass, when all Israel heard that Jeroboam was come again, that they sent and called him unto the congregation, and made him king over all Israel: there was none that followed the house of David, but the tribe of Judah only.
Jeroboam was of the TRIBE OF EPHRAIM, not Judah. Per 1 Kings 11, God ordained Jeroboam to be king over the northern ten tribes of ISRAEL, called the "kingdom of Israel". At that time of the split of Israel into TWO SEPARATE KINGDOMS by God's Hand, the tribes of Judah and Benjamin ONLY were together in the south and made up the "kingdom of Judah" per God's written Word! Solomon's son Rehoboam, of the tribe of Judah, of the house of David, was king over the "house of Judah", ONLY the tribe of Benjamin joined with Judah there at Jerusalem-Judea...
21 And when Rehoboam was come to Jerusalem, he assembled all the house of Judah, with the tribe of Benjamin, an hundred and fourscore thousand chosen men, which were warriors, to fight against the house of Israel, to bring the kingdom again to Rehoboam the son of Solomon.
KJV
A SMALL REMNANT of the northern ten tribes migrated south to join with Judah and Benjamin, because they refused Jeroboam's calf idol worship he setup among the ten tribes to keep them from going down to Jerusalem to worship. Jeroboam also made common priests of the people among the ten tribes, which made the Levites in the north leave also, and go south to join with Judah and Benjamin. Those of the SOUTHERN "KINGDOM OF JUDAH" THUS BEGAN TO CALL THEMSELVES 'JEWS', the Jewish historian Josephus said that title of 'JEW' came from the sole tribe of Judah's name.
THUS THE TITLE OF 'JEW' BIBLICALLY ONLY APPLIED TO THE TRIBES OF JUDAH, BENJAMIN, AND LEVI, AFTER THE SPLIT OF OLD ISRAEL INTO TWO SEPARATE KINGDOMS. And that is where Apostle Paul's claim of being a 'Jew' comes from, because Paul was actually born of the tribe of Benjamin, like he said. Josephus said ALL those living in the southern lands of Judea began calling themselves by that title of JEW, even the foreigners that lived there. So in reality, the title of JEW, or Judean, began as a geographical title, like regardless of one's origin of birth if they live in Texas they can call theirself a 'Texan'. And likewise today, anyone of any national origin that converts to Judaism, can call theirself a JEW.
But the Israelites of the NORTHERN KINGDOM OF TEN TRIBES, the "house of Israel" or "kingdom of Israel", they did NOT use that title of JEW. Josephus made that distinction when he showed that the remnant that returned to Jerusalem from the 70 years Babylon captivity called themselves by the title of JEW.
And once God removed... the ten northern tribes of the "house of Israel" OUT... of the holy land by the kings of Assyria, that LEFT ONLY THE HOUSE OF JUDAH IN THE LAND, at Judea! (2 Kings 17).
1 Kings 12:19-21
19 So Israel rebelled against the house of David unto this day.
20 And it came to pass, when all Israel heard that Jeroboam was come again, that they sent and called him unto the congregation, and made him king over all Israel: there was none that followed the house of David, but the tribe of Judah only.
21 And when Rehoboam was come to Jerusalem, he assembled all the house of Judah, with the tribe of Benjamin, an hundred and fourscore thousand chosen men, which were warriors, to fight against the house of Israel, to bring the kingdom again to Rehoboam the son of Solomon.
KJV
1 Kings 12:17
17 But as for the children of Israel which dwelt in the cities of Judah, Rehoboam reigned over them.
KJV
2 Kings 17:18-24
18 Therefore the LORD was very angry with Israel, and removed them out of His sight: there was none left but the tribe of Judah only.
That was per 1 Kings 11. God split Israel into TWO SEPARATE KINGDOMS, and made Jeroboam of the tribe of Ephraim king over the northern ten tribe "kingdom of Israel" with its capital city at Samaria in the north. Judah and Benjamin made up the southern "kingdom of Judah" at Jerusalem-Judea.
19 Also Judah kept not the commandments of the LORD their God, but walked in the statutes of Israel which they made.
20 And the LORD rejected all the seed of Israel, and afflicted them, and delivered them into the hand of spoilers, until He had cast them out of His sight.
Then about 120 years later, the "house of Judah" that was left in the holy land began to fall away too, so God brought the king of Babylon upon them to took them captive to Babylon for 70 years. NONE of that involved the ten northern tribe majority that had before already been removed to Assyria and the lands of the Medes (2 Kings 17).
21 For He rent Israel from the house of David; and they made Jeroboam the son of Nebat king: and Jeroboam drave Israel from following the LORD, and made them sin a great sin.
22 For the children of Israel walked in all the sins of Jeroboam which he did; they departed not from them;
23 Until the LORD removed Israel out of His sight, as He had said by all His servants the prophets. So was Israel carried away out of their own land to Assyria unto this day.
That was about the NORTHERN TEN TRIBE "KINGDOM OF ISRAEL" ONLY, not the southern "kingdom of Judah" (of 3 tribes). Judah remained in the land, like verse 18 said!
24 And the king of Assyria brought men from Babylon, and from Cuthah, and from Ava, and from Hamath, and from Sepharvaim, and placed them in the cities of Samaria instead of the children of Israel: and they possessed Samaria, and dwelt in the cities thereof.
KJV
Then as was a trait that the kings of Assyria did to a conquered nation, they moved foreign peoples in place of the ten northern tribes that they took captive to Assyria. And these foreigners came from five different provinces of Babylon, and became known as the Samaritans.
After God had removed the ten northern tribes, only the tribes of Judah, Benjamin, and Levi were left in the holy lands, and they called theirselves JEWS, which title originated from the name of the tribe of Judah. With the majority of the ten tribes gone, and LOST, the JEWS only were left, and many of them began to FALSELY CLAIM THEY ONLY REPRESENT GOD'S ISRAEL.