That Shoghi Effendi did not write a Will was due to the circumstances of his ministry and of his life. It must be realized that he was a most meticulous person who never left anything to chance, especially in the case of such a vital issue as writing his Will and Testament to appoint a successor to himself. Only through reflection will a believer come to appreciate the wisdom and inevitability of Shoghi Effendi remaining silent on this question.

One of Bahá’u'lláh’s injunctions in the Kitáb-i-Aqdas is that every Bahá’í should write a Will and Testament, and that foremost in it he should bear witness to the oneness of God in the Dayspring of His Revelation, Bahá’u'lláh. This confession of faith is to be a testimony for him in both this world and the next. A Will also directs the distribution of wealth among one’s heirs. As to the first requirement, Shoghi Effendi’s letter entitled The Dispensation of Bahá’u'lláh is one of the finest declarations of faith ever written. No believer has written such an outstanding confession of his religious beliefs as Shoghi Effendi did in this remarkable document. As to the second part of a Will, which is the bequeathing of a person’s wealth to his inheritors, Shoghi Effendi did not have any worldly possessions and therefore had no need to distribute them. Thus, it can be said that he carried out the commandment of Bahá’u'lláh with regard to the writing of a Will.

As to the appointment of a successor, the Master had stated in His Will and Testament that should the ‘first-born’ of the Guardian not inherit his spiritual qualities, he should appoint another Ghusn (Branch). The word Ghusn has been used by Bahá’u'lláh to signify His male descendants exclusively. ‘Abdu’l-Bahá was designated as  379  Ghusn-i-A’zam (The Most Great Branch) and Shoghi Effendi as Ghusn-i-Mumtaz (The Chosen Branch). Shoghi Effendi was not in a position to appoint a successor to himself because he had no son and there was not a single Ghusn who was faithful to the Cause of God. Every one of the descendants of ‘Abdu’l-Bahá had been declared a Covenant-breaker.

Not only was Shoghi Effendi unable to appoint a successor to himself, but his hands were also tied in making a pronouncement about it. This is because Shoghi Effendi was the Interpreter of the Word of God. This allowed him to explain everything which was in the Writings of Bahá’u'lláh and ‘Abdu’l-Bahá and apply their teachings and commandments within the framework of the exigencies of the time. However, what Shoghi Effendi could not do was to pronounce on subjects which were not recorded in the Holy Writings. These fell within the purview of the Universal House of Justice, which alone has the authority to legislate on matters which are not revealed by the Pen of Bahá’u'lláh or ‘Abdu’l-Bahá. Since the Will and Testament of ‘Abdu’l-Bahá did not indicate the course to be taken should there be no Ghusn (Branch) to succeed Shoghi Effendi, the resolution of this question did not fall within the domain of the Guardianship; it was the prerogative of the Universal House of Justice to find a solution. This is probably the main reason why Shoghi Effendi did not make any statement about his successor.
Adib Taherzadeh, The Covenant of Bahá’u’lláh, p. 378

The weighty treatise known as The Dispensation of Bahá’u'lláh , written in 1934, burst upon the Bahá’ís like a blinding white light. I remember when I first read it I had the most extraordinary feeling as if the whole universe had suddenly expanded around me and I was looking out into its dazzling star-filled immensity; all the frontiers of our understanding flew outwards; the glory of this Cause and the true station of its Central Figures were revealed to us and we were never the same again. One would have through that the stunning impact of this one communication from the Guardian would kill puniness of soul forever! However Shoghi Effendi felt in his inmost heart about his other writings, I know from his remarks that he considered he had said all he had to say, in many ways, in the Dispensation.
Ruhiyyih Khanum, The Priceless Pearl, p. 213 (Ocean)