Should we actually be looking at a data migration out of these SQL 2000 DB's first, into a newer SQL DB, and then backup and archive.....
Yes correct that would be correct approach.
or are there means to still restore a SQL 2000 DB backup file into newer versions of SQL like 2017.
No you cannot restore SQL Server 2000 DB backup directly no SQL Server 2017. You have to first upgrade to SQL Server 2008 r2/2008/2005 ( I would suggest SQL Server 2008 R2) and then move to SQL Server 2017.
As I see here if you need the databases data after every 5-10 years then you must upgrade the database to latest version SQL Server 2019 and then take backup on tape and store the tapes. You have to repeat above task to make sure data is moved on latest version and stored.
Don't worry about restoring database. It is not a cumbersome task. A simple google search will help you in restore if needed.
EDIT: From questions you posted later
If I were to take a backup of a Windows 200 Database, and then try to restore it to a Windows 2017 SQL instance, for example, then would that Database just not restore at all?
Yes you would not be able to restore. Moving data out from table is little tricky task as compared to restore.
I presume that is needed because in every one of those stages there are new Database schema additions\attributes added to the customer databases along the way? And without those additions at every stage, the later versions cannot mount the Databases......something like that?
There is no schema addition neither any attributes that i know. The restriction is put from MS side may be because of some internal challenge which I do not know
The point is you can turn it as a diff billable project to upgrade to 2019 but that is up to you and your business. The thing is later even of you have .bak file for SQL Server 2000 unless you have 200 DB engine you would not be able to read it. So put that in front of client, inform him about all the risk and let him take decision.