For the record, I don't think this is a good solution and I support continued use of "century" and "millennium" as they are the most intuitive ways for editors to enter this information. It's also the way that date information is recorded on Commons and it will be important that Wikidata support that for the Structured Data on Commons project. Perhaps Wikidata just needs to change how it parses these dates (i.e. T73459).

The actual bug is that some software (such as the Wikidata user interface) doesn't seem to be following the definition of the "precision" field in a date.

Precision, as described at https://www.wikidata.org/wiki/Help:Dates, specifies how many digits of the date string should be ignored.

E.g., +2018-06-00T00:00:00Z is not a valid date, but with precision 10 (month) it specifies the range 2018-06-01 to 2018-06-30.
With precision 7 (century) it specifies the range 2000-01-01 to 2099-12-31. When this date is entered into a Wikidata field and precision set to 7, it displays "21 .century". This would be OK if it was generally accepted that Wikidata takes the century as 2000-2099, and not 2001-2100 as is sometimes used.

However, if the date +2000-00-00T00:00:00Z if entered with precision 7, the user interface displays it as "20 .century", which is now confusing everybody. I suggested avoiding the word "century" entirely.

@Ghouston: Thanks for clarifying that!

I don't know which bug is the correct one, so I'll quote myself.

In T73459#4295225, @Jc86035 wrote:

Would it be difficult to display this as a range, like "some point in time between 1 January 2001 and 31 December 2100"? Or is there something in the way these are displayed which would make this technically impossible? (Doing this for dates with year precision, although not necessary, would be helpful in encouraging editors to increase the precision of the data they input.)

Current Wikibase definition of beginning and ending years of a century and millennium are in synch with the definitions in the English or German Wikipedia, see :de:19._Jahrhundert for example. Maybe Wikibase software could just provide a link to the item like Q6955 to clarify the definition, and where we can specify the date range.

In T196674#4430825, @Jarekt wrote:

Current Wikibase definition of beginning and ending years of a century and millennium are in synch with the definitions in the English or German Wikipedia, see :de:19._Jahrhundert for example. Maybe Wikibase software could just provide a link to the item like Q6955 to clarify the definition, and where we can specify the date range.

Wikibase is not a single thing. It is made up of many parts, and currently the user interface disagrees with all the other parts about what range is indicated when the precision is set to 7.

Link to the bot request to clean up time data with these precisions automatically because Wikibase won't do it by itself and no one's fixed it in five years

Since I commented above, https://www.wikidata.org/wiki/Help:Dates has been edited and now says that "Any date in range 1801-1900 with precision 7 is interpreted as 19th century". Does this resolve the inconsistency?

The change in the Dates help page was made by Jarekt at 14:28, 17 July 2018 UTC. The edit summary states

Switched text from what "should" be the first and last year of decade century or millennium, to what is currently interpreted by the wikibase software

I don't know about this edit, but other editors have been known to claim the wikibase software works a certain way, when what they really investigated was merely the user interface.