It seems that much of the basic training coming from Waseda University was a kihon version of kata. This is typically exercised with a static uke. In an attempt to create a more dynamic situation Kogure pieced together some techniques that demanded more movement.
Another of the angles this kata originally attempted to address was people coming in from a more distant ma-ai. In this way the kata also helped to teach students to deal with multiple attack situations. Many of the old timers I have seen perform this kata practice it with the attack as a straight armed run towards tori. Also, as a personal observation I see some more Ueshiba like techniques in this kata that were left out of Tomiki's curriculum such as a classical tenkan irimi nage and shizumi otoshi.
I personally have not seen evidence of this kata practiced by any Japanese or British dojos. From my casual observations this kata seems to largely be present mostly in American lineages of Tomiki Aikido. I believe this may be largely due to Kogure Sensei teaching in the United States from 1970-1975. In many schools in American Tomiki lineage branches it is required for shodan and nidan (1st and 2nd black) grading demonstrations. Typically the first five is demonstrated for shodan. The entire kata is often demoed for nidan.
So the original intention of the kata seems to have been to get attackers moving more dynamically when giving energy. Eventually the majority of kata practice grew to have a more committed attack, so practicing many of the techniques that were already in the 17 kata became somewhat redundant.
Some organizations dropped the redundant techniques and added others from aikido or judo. In other organizations the meaning of the kata began to morph in the 1970s and 1980s. Eventually the kata started being practiced with a go-no-sen timing. This gave it a new life and gave purpose to the techniques in the kata again. While the techniques of the 17 were often practiced sen-no-sen timing, the Big 10 started being practiced as the late timing kata. Other teachers saw this as a separating centers kata, as opposed to the 17 kata which were often closing centers. I have even attended lessons from teachers that teach the redundant techniques as henka, or variation from the standard kata taught. One organization now often refers to the kata as Ura waza - reversal techniques.
Needless to say the kata changed either techniques or fundamental intention to suit the various teachers, schools and organizations as the kata aged.
2. Kata-otoshi - shoulder drop
3. Ude-guruma - arm wheel
4. Hiji-guruma - elbow wheel
5. Aiki-nage - fitting in throw (Aigamae Ate)
6. Shiho-nage - four corner (all directions) throw
7. Ushiro-ate - behind (from the rear) strike
8. Kote-gaeshi - wrist turn
9. Ushiro-kubi-gatame - hold from behind (the rear)
10. Shizumi-otoshi - sinking body drop
Here is a demo by Nick Ushin Lowry of the KazeUtaBudoKai. He does a separation version here, very different from the late timing version I learned. He switched around the first two techniques, I am not sure if by accident or if he rearranged the kata around his own understanding.
Go here to see Lowry Sensei lecturing on the techniques.
Here are two gentlemen performing the first 5 of the Big 10. This often is a requirement for shodan.