For good reason. According to your 39 Articles, the Sacrament of Ordination is not a Dominical Sacrament (that is, you believe that it was not established by Christ, nor known to the Apostles - which kind of blows Apostolic Succession out of the water right there - how could the Apostles have passed on something they didn’t receive from Christ, nor know anything about?) - further, the Ordination ceremony itself does not include the intention to ordain priests as the Catholic Church ordains them.
Well, Apostolic Succession is, strictly speaking, not necessary for a church to be part of that ‘One Holy Catholic and Apostolic Church’ since the Apostolic teachings are also key. From a historical standpoint, Apostolic Succession promotes legitimacy and a connection to the Early Church. After all, the Anglican Communion has ecumenical relations with churches that do not claim direct Apostolic Succession. Personally, I believe Apostolic Succession is very important, but not completely necessary.
Also, perhaps, instead of using the language of the XXXIX Articles (which use archaic wordings and linguistics), it might be better to talk of Greater and Lesser Sacraments.
The Greater Sacraments (Baptism and Holy Eucharist) are commanded of the Believer (as a Free Grace theologian, I do not believe that Baptism and Eucharist are strictly necessary for Salvation/justification, but they convey important sanctifying grace and Baptism kind of officially welcomes an individual into that One Holy Catholic and Apostolic Church and I would question why any Believer would, upon realizing that these things are commanded by Christ for the edification of the Believer and the Church, not want to be Baptized and partake in the Lord’s Supper).
The Lesser Sacraments (Confirmation, Holy Matrimony, Reconciliation of a Penitent, Holy Orders and Anointing of the Sick) are not commanded of the Believer, but they are made available for the further sanctification and edification of the Believer and as a connection to Tradition (the Lesser Sacraments, while not directly commanded by Christ, are extrapolated from other Apostolic writings [the New Testament sans Gospels] and Church Tradition). For example, Reconciliation of a Penitent, while not strictly necessary for the forgiveness of sins (I would argue that confession of sins directly to God is not necessary to be forgiven/‘remain Saved’; however, it is necessary to remain in ‘fellowship’ with God and to avoid certain temporal punishments and sufferings), it affirms that forgiveness from God and spiritual healing (James 5:16). Obviously, not all Believers are called to marriage (Holy Matrimony) and the priesthood (Holy Orders).
As a caveat, for those who are Baptized as infants, Confirmation is necessary (or at least highly recommended) so that the individual can vocally profess and personally affirm their faith and beliefs.