Your post, though "1 year and three months on", is a good opportunity to provide an update on the "common code" for those who didn't follow the updates presented to the Steering Committee/Members' Assembly, and to go into some more detail about the potential uses of the budget id.
Update: the DAC WP-STAT recently approved the addition of several new codes to the CRS purpose codelist. These new codes are voluntary, which means not all donors/publishers have to use them, but those who want to can. You're right that the "common code" has died - after much technical work, we came to the conclusion that we would get a much better fit with country budget classifications by integrating the new codes into the CRS codelist than using a separate "common code". In the last report to the Members' Assembly on June 29, we suggested that the common code be deprecated and encouraged all publishers to start using the new codes where relevant (along with the capital expenditure field, which is also part of the "budget id").
By "national taxonomies" I assume you mean the national budget classification (also called charter of account)? Indeed, it would be ideal if they were all public - and they should, as this is a good public financial management practice. Now that we have agreed on the new CRS purpose codes, the next step in each country is to map these CRS codes to the national budget classification and see how they will use the map to interpret project data (e.g. integrate the mapping in their aid management platform). Ideally, this CRS-budget mapping should also be made public, so that anyone can use it when looking at project data.
Franckly, with the new CRS codes, I think the match to individual country budgets will be much improved, while preserving cross-country comparability, which is also very important. As such, I wouldn't see much value in coding directly to country budgets. Similarly, the budget can help identify which national development priority, or which SDG, a project contributes to - making the CRS sector codes much more useful than perhaps they seemed to be.