I think that obtaining a Letter or not, would depend on one's interest or purpose or reason for doing it.
If it is done as a 'Gamble', betting/wagering in effect, the cost of the 'Letter' against the possible gain in value for the Arm, were it to have a demonstrated original provenance to a famous person or group or Business or something, then, one will either 'win' or 'loose' the bet...or one will win or loose by degree.
If it is done to see if the Gun 'Letters' to have the same features as it has now, then, one will ( probably ) find out if it was shipped with the Barrel Length, Finish, Stocks, Calibre/Cartridge designation, or whatever else, as one notes it to have now.
If it is just to see who or where it was originally shipped to, because one is curious to know, and one feels the cost of finding out is worth it, just to see, with no special hopes about it, then, one would find that out.
The Few Colts I have, which I would be tempted to Letter, would be ones from the early 1900s. It would be fun and interesting to see who or where they originally Shipped to...but, I have not tried it yet.