If that's the case, would the same stamp used on a registered FDC have the same value or would it only have the value of 12.00 as a FDC?
What really drives the value is the collector base and what they think is better. This Prexie collector base (current and especially past) are responsible for the popularity and drive to get solo usage covers, first for Prexies then spilling over to many other stamp series.
What carries the value are the business or commercial
usage covers. In general, the FDC are covers made a souvenirs with just any stamp slapped on the cover to get the cancellation without regard to a proper rate usage.
So for your example, it is assumed that the 19 cent stamp was placed on the cover for the FD cancel, registered as there was extra postage that allowed paying a minimum registration fee of 15 cents leaving a convenience over payment of one cent. Many FDC of 18 cents and greater are registered due to the fact that is covered in the payment the stamp represents and the likely greater security and thus receipt of the FDC if it is passing through the mail and not done as a hand back. What would "prove" your 19 cent FDC would be of the high price would be the sender's receipt for registration which shows postage at 3 cents, basic registration at 15 cent and the 1 cent supplementary fee for unindemnified value.
Thus with FDCs only when the cover starts to look like a proper usage does the value start to climb. One example is the 11 cent solo paying the combine air and surface rates to Europe. Such FD covers are rare and carry a value in hundreds beyond the simple over paid domestic one ounce letter. This such cover is determined by the transit markings. Attached is an image of a cover showing the described rate. It is not a FDC, but FDCs of this rate exist but need all the transit marking to be considered as a "proper" use. I own this cover and passed on the FDC as I already owned this cover.
What further complicates this particular 11 cent usage on FDC is there are two versions of the FDC, one with out proper transit marking proving carriage to Europe and one with the proper transit marking showing actual carriage. Only the latter carries the premium price.
The best example of FDC value and non-FDC value is using the $5.00 Coolidge as an example. There are thousands of solo $5 FDCs. But there are no known solo commercial $5 covers. The closest to one is an item with a $5 stamp plus a meter strip for the balance of postage required. Depending on the day, that item sells for either four or five figures. The first true solo $5, commercial, likely would fetch between $10,000 and $20,000 perhaps more, today.
Your question also applies to other purely philatelic Prexie areas. First Flight Covers are purely philatelic and one from 1939 usually sell for a couple of dollars as they are not uncommon. However, there is one Prexie exception since the cover had a solo 10 cent Prexie COIL affixed paying the correct 10 cent (that day) rate to Botwood. What makes this item even more philatelic due to the first flight is that the first flight DID NOT follow the correct airmail route. Due to the volume of collector mail, the stops were change to larger airports in cities where the volume of mail could be handled (postmarked) without delaying the overall flight. ONLY that first round trip flight landed in the alternate cities, all other flights (at least until WWII interrupted) used the correct and intended cities for this airmail route. That said, this purely philatelic cover is valued at over $300, the catalog price of the 10 cent coil on any common
cover but no where near the $2,500 for a solo on an international post card or the $3,000 for a solo on an airmail cover to the Caribbean or Central and South America. Now why is that? It is because Prexie collectors view the 10 cent coil solo as so difficult they will accept a purely philatelic item which happens to pay the correct rate and was carried to the destination plus someone was willing to pay the premium price.
page 306 for the article regarding the illustrated item. The particulars of the route deviation for the first flight was overlooked or ignored by the author to avoid further underscoring the philatelic nature of this FF cover. The author did include the item in his multi gold award winning Prexie rate exhibit.