Arena 1000 is fine because it's not popular.
For Colo I would do 1.1k to 1.3k. I think it is reasonable to say that the majority of players can reach at least silver1 and probably even gold3 as long as you are not brand new.

Your calculation is also missing the gems you get from Heaven Hold Princess, which I guessed at around 100 a week.

Guild raid is 3 weeks so it is 530 gems/week.

And I think your event estimation is way way off with 500 a week?
Points event, which seem to be the most common events, give way more gems. Nari event for instance gave like 2.7k gems.
The previous Rah Empire event pretty much gave a very similar amount of gems, I think roughly 2.6k gems too (absolute max was close to 3k or something like that iirc).
Yes, the current roadmap gives a lot less gems. However, it also seems like roadmap events are a lot less common.
The next event is literally gonna be a points event, again.

So 1k+ gems from events/week is much more closer to reality imo.

And the total then is much closer to ~6.4k gems.