Excellent questions and also an excellent move from "contradictory" to "paradoxical" instead. That was the exactly right shift and the key to understanding the importance of structures and canons in ensuring or helping to ensure the spiritual and countercultural nature of the consecrated hermit's vocation.
Let me ask you some questions which should help me make my point: have you ever tried to nail jello to a wall? Ever tried to drink or even pour a cup of coffee without the cup? Have you ever tried to deal with mercury outside some kind of container or sleep on a feather "pillow" without the sewn encasement? Ever tried to live a productive life without a schedule, or a place to live or work or tools to work with? How about trying to live as a Christian without benefit of baptism or attempting to ensure a strong sacramental life without depending on "externals" like water, oil, unleavened bread, Scripture, or ordained ministry? Ever tried to take a long journey while avoiding the use of "externals" like roads, maps, gas stations, restaurants, or food stores? How about crossing a busy street at rush hour safely without regard to traffic signals or when there are no traffic laws? How about playing a violin sonata without the violin or the sonata or the technique and musical structure and rules for doing so? Similarly, have you ever tried to cook a complex meal without recipes, timers, utensils, or a stove providing assured temperatures (how about by using sticks and leaves over a campfire)? How did that work out for you? Better than it did for me, I hope!!
A few more questions: have you ever tried to live a consecrated life without being consecrated by God, or a married life (with all the rights and obligations intrinsic to this state of life) without being married? How about raising healthy children without rules or consistent norms; how would that work out do you think? And how does one play games with one's children and have fun doing it if the game has no rules or norms and play itself is "anything goes"? Finally, what would happen if I tried to grow vines without a trellis, the proper soil, water, and other nutrients, or taste/feel the effervescence of CO2 without a liquid in which this occurs? In other words, where do externals stop being merely external to something and instead become necessary for and sometimes even intrinsic to the thing itself? The simple fact is the more precious and fragile or frangible an activity or thing is, and certainly the more important, the more dependent it is on established norms, customs, rules, structures and "containers" of all sorts. Similarly, because we are embodied (historical) beings living our lives in space and time we need these "externals" for protection and health.
The dichotomy being drawn between externals and the spiritual in your own question is largely a false one. You see, in my life I need certain structures, relationships, and laws as well in order to live this vocation fully and faithfully. Others need some of these same things so they can truly benefit from this vocation, but also sometimes, truly serve it. These "externals" are not really merely external; instead they are part and parcel of the vocation itself. I am not merely called to be a lone individual, but a hermit and this requires I stand in the tradition of eremitical life known throughout the history of humankind. But beyond this I am also called to be a hermit living this life in the heart and in the name of the Church and for that reason certain "externals" like consecration, public profession, canon law, legitimate superiors and the ministry of authority, a Rule, and so forth are necessary for and also an intrinsic part of this vocation. All of these things serve this vocation and the God who is its source and ground. Can one be a hermit apart from these things? Yes, or at least yes to some of them. But one cannot be a hermit living this vocation in the name of the Church without them.
The thing is none of these supposedly "external" realities get in the way of the spiritual dimension of my vocation any more than the cup gets in the way of a cup of coffee, or a pillow encasement gets in the way of the feathers. Instead they make these things possible -- and capable of benefiting others. Just like I need a violin and the music for a sonata if I am to play a violin sonata, so too does a call to be a diocesan or canonical hermit require the church, canon law, and the mediation of both the call and the response. There is no call to such a vocation apart from these. My vocation was not a call I heard once in my mind, and responded to similarly once and for all. It is a call I heard, responded to in a definitive way and continue to respond to day in and day out in an embodied way. Canon 603 and my own prayer, work in direction, and life within the Church, sacramental and otherwise, continues to mediate that call to me and to receive my response. Not everyone needs all of this to live as a hermit, of course, but to live as a hermit in the name of the Church and with the rights and obligations which allow that vocation to take concrete shape in my life and the life of the church, one needs these things. Again, they serve this vocation and I am glad for their service.
Our God reveals Godself exhaustively as incarnate. God is exhaustively revealed (made known and made real in space and time) in an embodied way in the person of Jesus. Jesus' humanity does not get in the way of this revelation; it serves it!! It makes it possible! It is an incredible paradox, and something theologians throughout our history have struggled with. So too it is with the supposed "externals" of canon law, church, ministry of authority, liturgy of consecration and profession, vows, Rule, etc. These allow the call of God to be revealed day in and day out, not only to the hermit, but to all of those the hermit's life touches.
These things shape my life in significant ways, yes, but they are also shaped by my life and reveal the way God is at work in it. Canon 603 isn't merely an external for me but rather something essential to mediate the voice and presence of God --- and thus, intrinsic to it. The same is true of the relationships I have with my Directors, my local parish, diocese, and so forth. These help create a realm of profound freedom infinite in its capacity to allow my exploration of life with God alone. To remove them is like sleeping night after night with one's head in an unconstrained pile of feathers. While this analogy fails like any analogy, it would not be long before the pile would cease to be and the feathers would be lost entirely through my own movement, and sweeping, bedmaking, laundry, an open bedroom window or door, and 1,001 other things which are part of everyday life.