Regarding the idea that earlier Roman ordination rites were comparable to the Anglican rites, it doesn’t address the actual point concerning the defect of intention. Rome has held sacramental rites which even explicitly deny the sacramental effect to be valid and to not affect intention (which is just to generally intend to do as the Church does, even if you are wrong about what Christ’s Church actually does).*****
From what I understand, Anglican ordinations were deemed invalid by virtue of the actions of the first generation of Anglican bishops who broke the line. The bishops who broke the line were essentially Catholics who chose a to use a rite not approved by the Church for the very purpose of not doing what the Church does. They modified the rite to exclude the intention of the very Church they had acknowledged as Christ’s.
As Catholics, they were presumed to know which Church is the correct one. Their ordinations were invalid by defect of intent for the same reason that a marriage is presumed invalid when the couple is Catholic and doesn’t follow Church law (by choosing not to do what the Church requires, they manifest the intent to not do what the Church does), while Protestant marriages are not invalid when they ignore Catholic Church law. This is called the principle of positive exclusion.
If a Catholic uses a rite approved by the Church, regardless of his personal beliefs, he is presumed to have the proper intention. But those bishops themselves chose to change the rite to manifestly exclude that intention.
Later generations might have the proper general intention to do what Christ’s Church does (even if they are wrong about which Church is Christ’s and what His Church actually does), but the line was already broken.
*****Here’s an example where a Protestant rite explicitly said Baptism has no effect and where the minister mocked Catholics for being superstitious to believe it did during the rite. The Church held these Baptisms to be valid (sorry, I can only find it in Latin).
18 Decem. 1872
Vic. Ap. Oceaniæ Centr.
Dubium quoad Baptisma administratum ab hæreticis
In quibusdam locis nonnulli (hæretici) baptizant cum materia et forma debitis simultanee applicatis, sed expresse monent baptizandos ne credant Baptismum habere ullum effectum in animam ; dic*** enim ipsum esse signum mere externum aggregations illorum sectæ. Itaque illi sæpe catholicos in derisum vertunt circa eorum fidem de effectibus Baptismi, quam vocant quidem superstitiosam. Quæritur :
i) Utrum baptismus ab illis hæreticis administratus sit dubius propter defectum intentionis faciendi quod voluit Christus, si expresse declaratum fuit a ministro antequam baptizet, baptismum nullum habere effectum in animam?
ii) Utrum dubius sit baptismus sic collatus si prædicta declaratio non expresse facta fuerit immediate antequam baptismus conferetur, sed illa sæpe pronuntiata fuerit a ministro, et illa doctrina aperte prædicetur in illa secta?
Ad i. negative, quia non obstante errore quoad effectus baptismi, non excluditur intentio faciendi quod facit Ecclesia
Ad ii. Provisum in primo
vatican.va/archive/***/documents/***%2025%20%5B1892-93%5D%20-%20ocr.pdf (see page 246)