Why not dash or bash ?

Because bash can not be the default shell when it is not executable.

sh is a soft link of dash on termux, I read the code of login.in, it uses sh instead of dash.

Fair enough, this was added way long ago in 80905a2

ash probably still exist at that time https://android.googlesource.com/platform/system/core/+/master/shell_and_utilities/README.md

.../usr/bin $ chmod -x bash
.../usr/bin $ chsh
Changing the login shell
Enter the new value, or press ENTER for the default
        Login Shell [ash]:
/data/data/com.termux/files/usr/bin/ash is not an executable file!
.../usr/bin $

But it probably not exist now

Why not dash or bash ?

sh is just symbolic link to dash.

Also it looks for bash if available if you look in the line before it :)