Thanks for this question. It is a very good one and I think this is the first time it has been asked. The passage you are referring to in Paul Giustiniani reads as follows: [[Let our rule of life be the life of Christ; let our written rule be the Gospel, having it always in our hands, taking care never to stray from the very rules of Christ. Therein lies true religious life, the norm of all perfection. What is there in the rules of St Dominic or of Saint Francis that is not in the Gospel? Since we are Christian, let us renew ourselves, as by a new baptism, so as to follow Christ alone. What Saint Paul told the Corinthians applies to us: Did Dominic and Francis redeem us in their blood? Have we put on Dominic or Francis? Christ is the font of living water; all these saints are but tributary streams. Let us drink from the source. Let us follow along the royal road as they did, the One who has called us.]]
It is not presumptuous for the Church to ask hermits to write a Rule of Life with regard to canon 603, so long as we understand the way such a Rule functions, both for the hermit and for the Church herself. For instance, beginners in the eremitical life tend to write Rules which are legalistically focused; they are focused on law rather than on Gospel. Such Rules tend to be unliveable and in any case will certainly stifle growth in the spiritual life and the freedom of the hermit. Because dioceses use the Rules which are submitted to them as part of their discernment of the vocation standing in front of them, such a Rule could tell them a person is not yet ready for profession or that she needs more formation --- and possibly in what areas of her life. Someone who has lived eremitical life for some time and is both self-aware and disciplined enough to build what is critical to her life in Christ into her Rule, will write a very different sort of Rule than the beginner. This will be evident to those who read it, as will the degree of experience, formation, commitment, and vision (including all the ways the centrality of Scripture is embodied in the life) of such a candidate for profession.

Giustiniani wrote of St Francis and St Dominic as "tributary streams" from the primary "font of living water" that is Christ. Consider that Giustiniani knew full well that both of these Saints had either written or adopted Rules (Dominicans use the Rule of St Albert) which allowed them to make sure the Gospel was lived in a way which ministered to the times and people of these times. He does not condemn these Rules but he does clarify the place of Christ's own life and the Scriptures to them. In other words. like hermits writing Rules for c 603, their Rules do not replace the Gospel; instead these Rules involve a vision of a way in which people can allow the Gospel of God in Christ to predominate and speak to the people who would follow Christ in this specific way rather than in another. Had I written an eremitical Rule in the 16th C. rather than the 21st, it would likely look rather different than the ones approved by canonists in 1985, or with a Bishop's Decree of Approval in 2007, for instance, but it would still be a tiny tributary of the Living Water I know in Christ.
I think it's really important for a person to grapple with the place of Christ in their whole life and experience. Writing a Rule demands one do this in more disciplined and challenging ways than almost anything else I know except ongoing personal formation with one's director. It is similarly important for one to articulate their vision of the nature and place of eremitical life in the contemporary world and Church. Writing a Rule also forces one to do this to some extent while living the Rule encourages further reflection and inculcation or formation. Again, it is important that a diocese be able to have something which serves to assist them in discerning and establishing guidelines for formation for a vocation to solitary eremitical life. A candidate's writing of a Rule does that as well. And finally, it is important when dioceses and the larger Church evaluate the way Canon 603 is and is not being implemented that they be able to document the way hermits live their lives. The Rules hermits write and submit to their dioceses will assist with this as well; a copy of this Rule is kept in the hermit's file; it is not a purely personal document but a quasi public one.