(I haven't read the manga or novel, just watching the anime, currently at episode 7)
In episode 2, Elaina became a full-fledged witch & went to the Land of Mages. Upon arriving, she was told that witches are automatically allowed in because only witches could get in. Later in the episode, Elaina was rejected from every hotel she visited because she wasn't recognized as a witch since her brooch marking her status as a witch was missing. Add to this the fact that later in the series, people only recognize as "a witch" and not "that witch", meaning she's not famous, and that her status is only signified by having a witch's brooch.
Elaina was granted her brooch in episode 1 by Fran who was an unknown witch (at least in her area). Considering this, there's nothing to guarantee that the brooch was granted to Elaina for some illegitimate reason, such as a bribe, and that brooches can't be handed out without control, and that anyone with some money/status can just buy a witch's brooch.
Despite how there seems to be no anti-counterfeit, everyone seems to recognize anyone with a witch's brooch as trust-worthy & looked up upon, as shown by how people seem to invite Elaina (and later Niké) into their homes without question, as well as treat with great hospitality.
It'd be understandable in Saya's case, as she's recognized as "a witch from the United Magic Association", which seems to be a well-established group. However, Elaina appears to be part of no such reputable organization, and her main credibility as a witch comes from having a brooch, which seems to have come with no reliable backing.
Given such a lack of backing (in both ability & personality) for witches' brooches, how is it that witches are universally (so far) regarded so highly? (If this is answered later in the series, please mark your answer with a spoiler warning)