Indeed, many communities exist as individual communities on their own without a larger connection. However, this is not an easy path. The community has to exist on its own and find a wandering bishop to ordain for it and provide episcopal services. However, it is also true that it is not easy to belong to a group in our movement. Bishops in our tradition can be untrained, despotic, and overbearing. However, this is not different from any other Church where the bishop can be difficult. I recently saw the movie "Man of God," where St. Nectarios of Aegina was treated terribly by the Patriarch of Alexandria and suffered great persecution from the Synod. In fact, Nectarios was later canonized and the Patriarchate apologized for their cruel treatment.
Despite not being easy, it is necessary for communities to have a bishop. St. Ignatius of Antioch stated in his Epistle to the Smyrnaens:
"See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop."
In the early Church, there were likely presbyter-bishops and deacons who shepherded congregations. As Christianity grew, bishops became monarchical and the three-fold ministry became predominant with priests as an extension of bishops. The deacon is also connected in a special way to the bishop. Bishops were responsible for consecrating other bishops (with 1-2 others), ordaining priests and deacons, as well as shepherding the regional church. There is the exception of the Church of Alexandria who ordained their bishop through the laying on of hands of priests, but this appears to be an exception and died out relatively quickly.
In the Old Catholic tradition, Varlet provided the episcopacy to the Church of Utrecht out of necessity and the church continued through its people, clergy, and bishop. This was affirmed by the Statute of the International Bishops' Conference in 2000 which said (emphasis mine):
"[the local church is a] communion of people, which by the reconciliation in Jesus Christ and by the outpouring and the continuous work of the Holy Spirit is constituted as a unity in a given place around a bishop with the eucharist as its center."
Dr. Esser affirms "The bishop is the sign of unity in his church. The spiritual centre of this unity is the Eucharist, in which the bishop represents the crucified, risen and real present Christ in the congregation. He is the real leader of the Eucharist. The priests in the parishes actually celebrate 'only' being commissioned by the bishop and acting in his place." He goes on to state that Urs van Arx defines the specific Old Catholic charism of the episcopate being "personal, collegial, and communal." 1
Of course, this is complicated in Independent Catholicism. There are hundreds of "wandering bishops" which present challenges to organizational structures (although I do see parallels to bishops of dicasteries and diplomatic missions). But, becoming a bishop is so accessible in Independent Catholicism there are not a lot of reasons to not have some affiliation to a bishop. It is also not outside the realm of possibility that the pastor of a large congregation becomes a bishop in the early church model, surrounded by priests (presbyters) and deacons. Or, even a loose association can be worked out where a congregation has a tie to a bishop who has oversight (even while the congregation maintains autonomy). However, for Catholics the episcopacy is necessary even when it is difficult.
1: Episcopacy - conciliarity - collegiality - primacy: the theology and the task episcopacy from an Old Catholic perspective.