How long will Tesla still need Cobalt? No sure way to know as they play their battery chemistry and improvement path so close to the vest.
JB stated back in 2016 that Co supply was of more concern to him than Li, and suggested they were going to try to increase the amount of nickel used in their cathodes to reduce amount of cobalt in their NCA cells.
A good primer on leading cell chemistries and percentages of metals is in this link to Electrek back in 2016.
Breakdown of raw materials in Tesla’s batteries and possible bottlenecks
It shows typical NCA chemistry cells contain 15% cobalt, 5% Al and 80% Ni. Back then Co price was $27,000 per tonne. Nickel around $10,000 per tonne. Tesla NCA breakdown % likely is slightly different. If cell chemistries without Co can match performance of EV batteries with Co, that is both a substantial cost saving as well as eliminating a serious supply constraint and PR problem. The savings which are possible by eliminating Co are too big to be ignored by companies trying to get to lowest possible KWh battery costs.
Note the LMNO chemistry is not shown in the Electrek article, probably because it wasn't in commercial use already. There are likely several competing paths toward minimizing or eliminating Co in EV batteries.
The next is total speculation. I'm guessing that these no cobalt chemistries have not become viable until very recently and would be too big a risk for Tesla to use for what we believe is the much improved energy density for cells planned for Semi and Roadster. I think perhaps they are being developed for two or three years farther out as a component of additional cell/pack KWh cost cuts by 2021.
IMO from studying online Nano One information and other sources, replacing one Li cathode chemistry with a different one is not as huge a production change as one might think once sufficient testing and tweaking is complete.* The cathode manufacturers would provide newer cathodes in same physical size package to Panasonic/Tesla and others. Moving from liquid electrolyte to a solid would seem to be a more difficult change as the machinery used for physical prep and rolling of the cells would need redesign.
* Jeff Dahl's group have developed greatly superior testing methodology and hardware than what has been available until now. That testing capability should give Tesla a good edge over competitors in determining when a revised chemistry (or nano level improvements to same chemistry) are ready to go ahead to production.