And for the sake of completion, why would a magus want to not join the Order?
Is it simply that the minor obligations to your tribunal and the Order at large are so unbearable to some as to outweight the protections and advantages you receive in return for putting up with them? In the 13th century and after, are there really any hedge wizards out there who practice a magic so powerful that it's worth risking your life to keep it secret?
The Order forbids a fair number of things you might want to do. If you've got a comfortable position as a court wizard, or are busy scheming to make your brother the Duke of Wherever, joining the Order might be an impediment.
A lot of hedge wizards joining the Order are going to be doing so as second class citizens, looked down upon by "proper" magi who've been Hermetically trained.
Regardless of the actual power of their magic, some hedge traditions might utilise a "leave and die" policy.
If there's a Flambeau in front of you telling you to join or be burnt to a crisp, these may not be sufficient motivation (or they may be!), but HoH: Societates (page 8 ) implies that a lot of invitations are a bit gentler than that.
Another potential reason would be that the magus is religious and/or want to join the clergy. The magus might be convinced that their power is a gift of god, and thus use it to carry out gods work / spread gods word.
Or maybe the magus prefers to dabble with the occult. Or some other form of forbidden / frowned upon type of magic.
Maybe the magus is trying to develop a new type of magic, and in trying to do so the magus wants to experiment on fellow mages. Being part of the order would certainly give you easier access to mages. But it also would expose you to a much higher level of scrutiny by your fellow peers.
One of the criticisms of hermetic magic is that it's so structured and by its nature tends to stamp-out a person's unique approach to magic. It is less "magical".
Perhaps the magus hasn't heard of the order, or doesn't think of what they do as magic. If they are gently gifted they might not want to associate with "those odd people" and keep their own abilities secret. Perhaps they were initiated into a secret tradition at a very young age and didn't have any more choice in the matter than a standard hermetic apprentice. Perhaps the fact that Magi of the order so seldom have children (due to the longevity rituals) that they assume there must be some sort of celibacy pledge involved...
Hermetic magic is relatively difficult to learn if you already know a hedge system. Joining gives your apprentices ready access to Hermetic magic, but at the cost of some, much, or all of your tradition. This is not likely to be appealing for members of the remaining traditions.
If you want to have influence in the mundane world, joining an organisation that prohibits interfering with mundanes would seem stupid. The Virgilians / Augustan Brotherhood would never agree to abandoning their ideas of a better world with court magicians acting behind the scenes. Likewise Volkhvy in the Novgorod tribunal, and spellcasters integrated into their communities/clan structures might see a forcible separation from their community as a really bad thing.
Those aligned to the realm of Faerie rather than magic (those with powers from RoP:F) would wonder what "Molesting the fae" could be taken to mean, and have hesitations about joining an order that could declare what they do illegal.
Those with infernal inclinations wouldn't join until they'd figured out a way to not get caught.
I can imagine some wizards with apotropaic magic that bargains with or tries to control dark fae or infernal forces to keep them away from their community thinking "so you want me to take my powers and not use them to protect my people, like we've always done?"
There's also the historical question for some - those shapechangers related to the Pomeranian shapechangers, witches related to the witches of Thessaly, Amazons who have heard from Viea, a surviving Hyperborean tradition that hid from Trianoma and Tremere, Sahirs who have faced Flambeau persecution - all of them will have heard tales of enmity with the order and have good reason not to trust offers to join.
There could also be some determined to go their own way and not answer to "foreign wizards" - oh, now I'm thinking that the Schism War was down to Diedne threatening to quit the Order and the threat of "Di-exit" causing trouble across Mythic Europe....
The majority of magi are not gentle gifted. People will be hesitant to join a group that they don't trust regardless of how good of a deal they offer.
"Our apparent shiftiness is just a byproduct of our gift. Once you start performing our secret ritual (that you can't know anything about until you sign up with us) on yourself this feeling will go away." is not a completely ideal recruitment statement.
A mage or a community (where one or more mages reside) could also be very isolated geographically and thus never been exposed to the Order of Hermes / know of them.
"4 out of 5 sets of entrails agree - My joining your Order will spell calamity for all of Mythic Europe. The fifth indicates its only the Order that will suffer." ?