In any case, from the baroque era there is no evidence of "holes" even in the instruments from various museums. I attended a course on natural trumpet building last year and made one.
We all had the good luck of having Jean-Francois Madeuf at the course. He performs all of the baroque stuff without holes and has many compelling arguments as to why it is better that way.
Still, the holey trumpets have a good purpose: they allow players that do not have the time for the high degree of specialization to get most of the "effect" of the older playing style. The sound is much different, but only the specialists make a big deal about it.
Here are some links to Jean-Francois' amazing playing (live performances - not edited recordings!):
Nr 64 Christmas Oratorio Weihnachtsoratorium Baroque Natural Trumpet without holes Barocktrompete Naturtrompete ohne L÷cher 21 12 2008 Hannover - YouTube
Nr 8 Christmas Oratorio Weihnachtsoratorium Baroque Trumpet without holes Jean Franšois Madeuf Konzert 21 12 2008 Hannover Jean Franšois Madeuf - YouTube
Bach BWV1047-3 - YouTube
It is "proof" that we do not "need" the holes, but that many more players will have access to a closer representation of the period IF we do have them!