Should It Be Called Christianity? Isn't "The Church" more appropriate?

I have been wondering why Protestants continue to allow the Church to be known collectively as "Christianity".  I know that we have just gotten used to the term, but I wonder about the validity of the term from a biblical perspective - which is the best perspective us Protestants can muster.

To begin with, in the Book of Acts 11:26 we find out that "the disciples were called Christians first at Antioch" and in 26:28 we read Agrippa asking Paul, "Do you think that in such a short time you can persuade me to be a Christian?"  The only other place where the term "Christian" is used in the biblical text is in 1 Peter where it is written:

If you suffer, it should not be as a murderer or thief or any other kind of criminal, or even as a meddler.  However, if you suffer as a Christian, do not be ashamed, but praise God that you bear that name.  (1 Peter 4:15-16)

So, the Bible uses the term "Christian" 3 times (twice in Acts and once in 1 Peter).

We find that in the Book of Acts the term "the Way" to describe the movement happens 6 times (as opposed to the two times in Acts when "Christian" is used - and in Acts you should note that the term "Christian" is not used by people who are part of the movement - which is a significant point).

Finally, the term church, to describe the movement that can be equated with "the Way" appears in the Book of Acts 20 times and in the Gospel of Matthew 3 times - other places the term appears in the New Testament are:

Romans (5)

1 Corinthians (23)

2 Corinthians (9)

Galatians (3)

Ephesians (9)

Philippians (1)

Colossians (4)

1 Thessalonians (3)

2 Thessalonians (2)

1 Timothy (5)

Philemon (1)

Hebrews (1)

James (1)

3 John (3)

Revelation (20)

This means that the term "church" or "churches" (other than titles for subplots within the larger narrative) appears 113 times, whereas "the Way" appears 6 times and "Christian" appears 3 times.  The term "Christianity" you'll also note, does not appear in the Bible.

I am just saying that, at least from a biblical perspective, the normative understanding of the life of the disciple of Jesus Christ is understood as "the church" a collection of people summoned by Jesus Christ into his ecclesia - his political gathering.  Thus, it would seem to me that the modern world's way of trying to understand "Christianity" is out-of-sync with the way the biblical witness seems to self-identify the movement.  Furthermore, the contemporary church does not seem to understand discipleship and community in the same way that the biblical writers understood, for they seem to favor "the church" (a community gathered in the name of Jesus Christ) whereas we tend to favour "Christianity" (a group of individuals with their own agendas gathered in the name of Jesus Christ).

Perhaps I'm a bit blunt, but I wonder if you see any of my logic?  Would your train of thought lead you down the same road as me or would it lead you down a different pathway?