New Orthodox Missions spring up, really, all the time. The U.S. is full of 'em (as well as many other non-historically Orthodox lands). They're quite vital, actually, because a new mission is how the Church comes to reside in yet another city. While people in a certain area may discover a parish and convert, it is important to plant new missions in other places as well, that a previous "unserviced" or "untouched" area would have an Orthodox presence and develop itself as a parish (which from the Greek simply means something like "neighborhood" or "community", lit. "para" + "oikos").
How do missions start? There are probably as many stories of how missions begin as there are missions. Every community has it's own history. My parish came into the Orthodox Church already as community of Christians, members of the Evangelical Orthodox Church. The parish was received into the OCA wholesale under the omophor of Abp. Dmitri of Blessed Memory. Other times, a group of people (usually several famlies, if a mission is to succeed) will inquire to the closest parish and, upon deciding to convert, will begin working to establish a mission where they already live instead of moving to a parish. The nearest parish will catechize, baptize and chrismate them. Then, they will find a space for worship and hold reader's services, usually a priest will come for Liturgy every once in a while. Eventually (God-willing), the mission will be sent a full-time priest, gain full parish status, and build a permanent Orthodox temple for worship. These are just some examples of how missions start. Again, there are probably as many ways to start a mission as there are missions!
You mention that, " It is my understanding that not just anyone can plant an Orthodox church like you can a protestant church. Why not exactly?" In a way, this is true. Anyone can petition the Church to establish a mission, must this must receive the blessing of the local bishop to proceed. Why? Because the Church is not some loosely-affiliated group of folks who sit around and read old books whilst eating bread and drinking some grape juice. The Church is a visible body, established by Christ and led by the Apostles, who have ordained their successors that have come down to us into the present day in the episcopate. The unity of the Church is in the bishop, who is surrounded by his priests, deacons and people.
In short: no bishop, no church. Period. ecclesiology is sacramental in Orthodoxy. The office of bishop is endowed with a certain role, a certain grace, as are the priests, deacons, etc. You can't have sacraments, for example, without a priest (baptism in extremis being an exception). No priest, no Eucharist, no chrismations, no marriages, etc. And priests are always attached to and assigned from a bishop...they serve at the behest of their hierarch. So, again...no bishop = no priest = no sacraments = no church.
But anyway, to go back to your original question: Yes, new missions exist and are founded all the time, particularly in historically non-Orthodox areas. You won't find as many in, say, Greece...Orthodoxy has had a firm hold on the population there for quite some time! But, places where the church is growing, they're everywhere! There's probably one that isn't terribly far from you (maybe further than you'd care to travel regularly, but still..."terribly" is a somewhat relative term!).