Well then I guess we have to assume that most/all agents don't have access to a tool that allows them to purge the field - all they can do is "add" a number.

Again, the tools are not necessarily designed to assist the flyer in your exact situation - having 2 or more "valid" frequent flyer accounts which they wish to be able to "switch" between at will - so you should not assume that you can do so.

In future, I would recommend keeping your bookings completely sterile. Do not log in with either your Skymiles or Flying Blue account while making any booking. Do not log in while looking at or checking your bookings - the app/website can or may associate an FFP number with a booking when you identify yourself in this way, EVEN THOUGH you never explicitly requested to associate that FFP number with that booking.

Only when you have determined which FFP to use with which booking should you then associate that FFP with your booking. (and yes, that may mean waiting for a long time, and foregoing the ability to pick from the best seats - but if your end goal is to have miles in a certain programme, you either need to stick with your first decision, or else wait until you know you won't want to change your mind again later).

But seriously, is it actually a good idea to keep both a Flying Blue and a Skymiles account? I know there are people who obsessively want to earn each flight (or each ticket) in whichever programme gives them the numerically-largest amount of miles - but when you are topping up two separate buckets with sporadic dribs and drabs, it takes you longer to fill any single bucket to achieve a usable amount. For example, if getting 300 miles in Flying Blue rather than 200 miles in Skymiles is a motivator to put a particular flight in Flying Blue rather than Skymiles, are you not overlooking the fact that you can't actually do anything useful at all with the "extra" 100 miles going into a semi-orphan Flying Blue account; 200 Skymiles (if that's your primary account) might actually be far more useful than 300 Flying Blue miles stranded in a Flying Blue account which will require many further thousands of miles before you can do anything with the balance - and bear in mind, FB miles expire.

Also, by topping up more than one Skyteam member frequent flyer programme, you are making it harder to reach or maintain status in any single programme (but good for you if you travel so much that this is not a concern)