Not so arbitrary really as there are 7 planets visible to the naked eye. Well, 5 planets and 2 "lights" to be precise but each day is named after one of these. The reason we don't get all this is that we're so out of touch with planetary cycles. We obsess over micro-measurements on terminals with ever more powerful technology yet can't see what is right under our noses.
What is more fundamental to earthly time than the rotation of the earth and its orbit around the Sun. From there it follows that the cycles of the other planets may also be important. I don't see how any of this is arbitrary. Isn't it amazing, for example, that Jupiter's cycle is 12 years and there are 12 lunations in a year? The cycle of Uranus is 84 which is 12 x 7. There's also a subtle mathematical relationship between 12 and 7. 12 = 3 x 4, 7 = 3 + 4. You have to have eyes to see these patterns.
> What is more fundamental to earthly time than the rotation of the earth and its orbit around the Sun.
True.
> From there it follows that the cycles of the other planets may also be important.
Not particularly, no.
> Isn't it amazing, for example, that Jupiter's cycle is 12 years and there are 12 lunations in a year? The cycle of Uranus is 84 which is 12 x 7. There's also a subtle mathematical relationship between 12 and 7. 12 = 3 x 4, 7 = 3 + 4. You have to have eyes to see these patterns.
None of that is amazing in the slightest, and your base numerology won't make it amazing.
You can find coincidences everywhere if your definitions are loose enough.