A great benefit of the Autocephalous Catholic movement is that it can be a home for former Roman Catholics. There are various people who have felt called to ministry but could not exercise it in the Roman Catholic Church. Similarly, there are laity who have been unable to practice their faith because they felt excluded because of their marital status, etc. The movement as a whole offers such variety that literally everyone can find someone or someplace that makes them feel they belong.
There is a downside, however, to attracting the (sometimes disgruntled) former adherents of another tradition. Inevitably, as is our human nature, they can want to re-mold it as "home." Suggestions are always helpful, and we can always improve. But when they are presented in a way that "I come from a 'real' church" or "I was trained properly because of my formation, seminary, etc." it can dampen the creative spirit of the Autocephalous Catholic movement. I have seen it happen before--former Roman Catholic priests (or priests from other traditions) believe they are the most important asset to a jurisdiction because their background or their experience. In reality, we are all just bumbling along on this trajectory called faith. Some may be more experienced or more educated, but it doesn't diminish the insight of the neophytes who are seeking to understand.
Because we are so local in our tradition, there is a real risk of forming communities which center around the personality of the priest. This can be especially risky when the priest brings most of their flock from a former parish. The connection can be to the priest rather than to the faith or the mission. This is, of course, not applicable to every priest who joins the movement. But it is something to monitor, lest the ministry or community suffer from being "a flash in the pan rather than a light to the world" in the words of Fr. Bjorn Marcussen.
Similarly, it is also problematic when people from other traditions bring along the anger and hurt they feel after isolation from their own tradition. I have sat through more than enough homilies about the "wrong that xx church caused me" or "how xx church needs to change" from clergy who were active in another jurisdiction. The reality is that once you've separated from it, you can chart your own course. This doesn't diminish one's experiences, but it does limit us from focusing on our former religious affiliation and centering our future around it. You have the freedom to follow your own spiritual destiny as you feel so called.
It is important to say that those of us who have been in this movement either from the beginning or for years do not have ways in which we can learn and grow. I was baptized in an independent Latin Mass parish and have been part of the periphery of Catholicism all my life. This has its own challenges and problems, as we can become blind to the problems that exist in our tradition. However, it does seem that those groups which adopt their own structures and traditions seem to be the ones that last the longest. Because there is a unifying ethos which brings them together, rather than a perspective of being "on the outside looking in" to another church.
My final thought is that it is impossible to not bring our own traditions and backgrounds into our spiritual journey. Every group has had its struggles when converts come in and bring their traditions to the table. The most apparent in my mind is the influx of former Evangelical Protestants into Eastern Orthodoxy. No transition is seamless, and we can learn from each other's experiences. But converts cannot presume that their way is the best way or that because they came from a more mainstream background that they are more experienced.