What was the point of the Babylonian captivity?

In the Bible the word used for thousands - eleph - is also used for small discrete groupings of tribes. So in the passage recounting the demands made by King Nahash at 1Samuel 11.1, it states of the armed force which came to rescue Jabesh-Gilead from the siege of the Ammonite king and possibly friend or ally of David (!); 'the children of Israel were three hundred thousand, and the men of Judah thirty thousand' (1 Samuel 11.8).

As mentioned by others, these numbers are not realistic; the largest empires/ armies of the era such as the Egyptian / Hittite Battle of Kadesh in c.1270Bce were at most 40,000 each side. Furthermore with regard to the Israelite number, there have been no archeological discoveries of any battle-site with such high numbers indicated. It is more likely that a/ the numbers given are symbolic ie hold metaphoric/numerical significance. The proportion of 10:1 making 11 in total is thus of interest. And b/ the term 'eleph' may be interpreted to mean small units of a tribe. Thus Israel had 300 units of around 50 men each representing an area or settlement, and Judah had 30 units of 50 or so men. This brings it to around one-twentieth of the translated value, making a total of around 16,500 men; a much more likely figure.

Re the Babylonian Captivity, the Old Testament makes clear the intention was to prevent further 'rebellion' - thus were all warriors, and metalsmiths in particular removed to Babylon (2Kings 24.14). Some commentators have proposed that Nebuchhadnezzar accumulated philosophers from all his conquered territories in order to force them to provide a way to 'transmute' metal into gold, for his enrichment. Quite a curious possibility. What the Hebrew priesthood and philosophers gained from their time in Babylon, learning the Sumerian /Akkadian and Babylonian cosmologies is another question entirely...

I'm going to guess you're coming at this with the idea in your head that every living soul in the country was exiled. That's incorrect.

In fact, while the Bible itself isn't consistent on the subject (and its our only real source), most likely what happened was something much closer to your "I could understand" option. We know the exiled included the King and his court, and quite a few others. We know there were in fact at least 2 deportations (reportedly 5 years apart). We also know it wasn't everyone, because when the exiles came back (after release by Cyrus), they were greeted by resident Jews.

Here's Moore and Kelle had to say on the difficulty of getting an exact number:

Overall, the difficulty in calculation arises because the biblical texts provide varying numbers for the different deportations. The HB/OT’s conflicting figures for the dates, number and victims of the Babylonian deportations become even more of a problem for historical reconstruction because, other than the brief reference to the first capture of Jerusalem (597) in the Babylonian Chronicle, historians have only the biblical sources with which to work.

^{Megan Bishop Moore and Brad Kelle, Biblical History and Israel's Past: The Changing Study of the Bible and History}

One thing is does look like we can say is that it looks like the Babylonians took the lion's share of the literate Jews with them. We know this because most of the rest of the Hebrew scriptures written from this point forward were written either in exile in Babylon, or by descendants of those who were. Which explains why it is today so easy to miss the detail that not everyone was taken.

The Book of Ezra does report there were about 42,000 people who returned from the exile in one wave, and about 5,000 in a subsequent wave. However, not all of those people were Jews, and this was 2-3 generations after the exile started, so we don't really know that a similar number were taken. And of course as historians we aren't allowed to take numbers from any one source as ... er ... Gospel, so we have to provide for the possibility that those numbers were inflated (or even deflated).