When I was a kid, it never occurred to me to ask why the disciples wanted to choose a twelfth man. Never. And then one day, later in my Bible learning days, I was part of a discussion where some guy claimed that the disciples were jumping the gun. His claim was that Luke's point in Acts was that the disciples chose Matthias, but God chose Paul.
That had seriously never occurred to me. His reasoning was flimsy, somewhat. And I thought his definition of 'apostle' was lacking, or at least was more narrow than the biblical range of meaning. Yet, I didn't have an alternate theory. It never occurred to me to ask. Honestly I still don't have a great theory, and merely critique the views of others. That critiquing is so easy is one reason I haven't come up with one myself.
If you use internal evidence, though, a theory may not be necessary. Let's look at the reason(s) Peter gives:
“Brethren, the Scripture had to be fulfilled, which the Holy Spirit foretold by the mouth of David concerning Judas, who became a guide to those who arrested Jesus. For he was counted among us and received his share in this ministry.” (Acts 1:16-17 NASB)
“For it is written in the book of Psalms,
‘LET HIS HOMESTEAD BE MADE DESOLATE,
AND LET NO ONE DWELL IN IT’;
and,
‘LET ANOTHER MAN TAKE HIS OFFICE.’
Therefore it is necessary that of the men who have accompanied us all the time that the Lord Jesus went in and out among us— beginning with the baptism of John until the day that He was taken up from us—one of these must become a witness with us of His resurrection.” (Acts 1:20-22 NASB)
If you have never checked Peter's references, he uses Psalm 69:25, and 109:8. If you decide to look those verses up, you find he didn't use the entire verse (to be fair, the Psalms weren't divided up into verses at that time). And if you check the context, you find one Psalm commonly thought to describe Jesus (Psalm 69), and another that certainly could (Psalm 109).
On the surface, if you don't check those Psalms, or check the context of what Peter used, you may think Peter is merely proof-texting. But context sort of supports his use. That was my first surprise. But the other surprise was more important. Look at the last sentence. There, right on the surface, is the reason for the twelfth man.
It wasn't to ensure they had someone to judge the twelve tribes in Judas' absence (at least one commentary had that one). It wasn't an error, jumping ahead of God who wanted Paul, because he couldn't be a witness to the entire life of Jesus. It wasn't any other of a dozen other options...ok, maybe two others. Anyway, what Peter says is actually what makes the most sense.
The only record of the life of Jesus was in those who were there, those who ate with Him, who walked, literally walked, with Him. Only they could attest to the words and deeds of Jesus while He was among His human creatures. Consider the words with which John ends his Gospel, where he claims that not all the words and deeds were recorded because that wasn't possible (John 21:25). We miss a lot because those witnesses are no longer among us.
But one question remains. Why twelve? There were obviously options among them who had been with Jesus in the period Peter describes. The people reduced the options to two, and God chose 1 of them to make 12. But why twelve? Maybe it was to round out the judges of the twelve tribes, but then, wouldn't their tribal heritage be important? Maybe it was to correspond to the twelve tribes of Israel. Although that simply runs into the same problem.
The truth, the reality we have, is that our Savior didn't think it was important to tell us why. Maybe the people of that day didn't need to be told, they had received that knowledge verbally already. Maybe it just sucks to be us, 2,000 years later, wishing we could be flies on walls of the early churches.
I think it's likely that this piece of the information, while interesting, isn't important to our Savior. He had His purpose, it was fulfilled in the choice, now move on. This is my theory. I don't know if I'm right or not, our Savior doesn't tell us. But there are a lot of other things He does tell us. I think I'll move on to those.