Right, because somebody already had one, not because they had just produced it.
Usually, ships with no affiliation are former CP ships, or ships the datacard for which was owned by a faction that dissolved, etc. Unique ships sometimes also say "no affiliation" even though they should say "rare".
There is no way to do so currently. The ones that currently exist are the only ones there will ever be unless something changes.
There have been some notable examples of this, however. The I-Beam starfighter for instance used to be a CP ship, but now it's a generic datacard and so it is producable again. The Dreadnaught-class Heavy Cruiser used to be a rare ship fetching enourmous prices, but it too is now a generic datacard.
Certain factions can buy Generic DC's, but being generic, they're not the only factions that can purchase them.
So for example, the X-wing DC, which is not a generic, is currently owned by the New Republic, who are the only faction who can make them.
The N-1 Starfighter however is a Generic DC, meaning that any production faction can build them as long as they purchase the DC.
It gives new production factions the ability to make a few ships, items, etc. Which is much better than how it used to be before the generic DC's were introduced, where production factions got nothing.
The "slots" for generic datacards pertain to their "cost" to factions that wish to purchase them. Factions with more active members get more slots, which they can fill with generic datacards. So factions can either choose more datacards that take fewer slots, or fewer datacards that require more slots.
That's not an easy question to answer. I doubt anybody expected rare ships including N-1 Starfighter and Dreadnaught-class to go from rare to a mere generic datacard pretty much overnight like they did. There's no telling what might happen, unless somebody with authority on the matter wants to chime in.
Personally, I hope that we haven't started a trend of turning CP ships into generics, as it ruins their collector value in-game. Imagine having something such as an Acclimator assault ship. An incredibly rare ship, which you acquired at tremendous personal cost. Then to find out it has been made a generic datacard and can now be purchased by anybody for dirt cheap prices?
I would therefore rather see, if more generics are to be added, they they be new entities rather than reused former CP ships. I don't personally think the addition of many more generic datacards will be likely, but who knows? R&D is allegedly a long ways off, so more may be added as a stop-gap until then. But I'm not on the dev team or anything, so what do I know?