From " 1.5.2. Goals for specific attacks to protect against" from the TUF spec:

Git protects against:

    * Arbitrary installation attacks. (Because metadata is signed)
    * Extraneous dependencies attacks. (Because metadata is signed)
    * Mix-and-match attacks. (Because a git commit hash depends on its parents)
    * Rollback attacks, assuming you make sure you only fast-forward when pulling.
    * Wrong software installation.

It does not protect against:

    * Indefinite freeze attacks. The attacker could 
      just replay the same signed git repository for a long time.
    * Vulnerability to key compromises. (Everyone can sign any commit, no separation)

It also has no built-in support for mirrors, and you cannot delegate trust to sub-maintainers easily, since any person who can sign a commit may potentially modify every file in the repo.

So I don't see how `git` is a valid solutions to the problems that TUF wants to solve.

Seriously, git is overused, actually misused, in places where it's a bad fit, just because we know it and it resembles some desired characteristics of the problem at hand. This then leads to package indexes which periodically cull the history and force-push the index. I'm sorry, but while some of the architecture of git may be applicable, just taking git and using it as a package index is plain wrong. Also, putting that much of a load on free github repos is not nice towards github's already regularly DDoS'ed network.

You can't think of it because you don't understand TUF's theat model.

Because it means downloading the entire history when all you want is the latest version.

When your only tool is a hammer everything starts to look like a nail.