What you call "conventional right view" is just skillful means to help one adopt a skillful or wholesome mindset. It's just a helpful tool. The following is an example.
“This noble disciple reflects thus: ‘I am not the only one who is the
owner of one’s kamma, the heir of one’s kamma; who has kamma as one’s
origin, kamma as one’s relative, kamma as one’s resort; who will be
the heir of whatever kamma, good or bad, that one does. All beings
that come and go, that pass away and undergo rebirth (upapatti), are owners of
their kamma, heirs of their kamma; all have kamma as their origin,
kamma as their relative, kamma as their resort; all will be heirs of
whatever kamma, good or bad, that they do.’ As he often reflects on
this theme, the path is generated. He pursues this path, develops it,
and cultivates it. As he does so, the fetters are entirely abandoned
and the underlying tendencies are uprooted.
AN 5.57
What you call "profound right view" are universal truths. Whether anyone is there to know them or not, they remain true.
“Mendicants, whether Realized Ones arise or not, this law of nature
persists, this regularity of natural principles, this invariance of
natural principles: all conditions are impermanent. A Realized One
understands this and comprehends it, then he explains, teaches,
asserts, establishes, clarifies, analyzes, and reveals it: ‘All
conditions are impermanent.’
Whether Realized Ones arise or not, this law of nature persists, this
regularity of natural principles, this invariance of natural
principles: all conditions are suffering. A Realized One understands
this and comprehends it, then he explains, teaches, asserts,
establishes, clarifies, analyzes, and reveals it: ‘All conditions are
suffering.’
Whether Realized Ones arise or not, this law of nature persists, this
regularity of natural principles, this invariance of natural
principles: all things are not-self. A Realized One understands this
and comprehends it, then he explains, teaches, asserts, establishes,
clarifies, analyzes, and reveals it: ‘All things are not-self.’”
AN 3.136
What about the fully enlightened ones? What views do they hold?
The answer is that they have let go of all views.
"A person who associates himself with certain views, considering them
as best and making them supreme in the world, he says, because of
that, that all other views are inferior; therefore he is not free from
contention (with others). In what is seen, heard, cognized and in
ritual observances performed, he sees a profit for himself. Just by
laying hold of that view he regards every other view as worthless.
Those skilled (in judgment) (i.e. the Buddhas and their disciples who
have realized the goal). say that (a view becomes) a bond if, relying
on it, one regards everything else as inferior.
Therefore a bhikkhu
should not depend on what is seen, heard or cognized, nor upon ritual
observances. He should not present himself as equal to, nor imagine
himself to be inferior, nor better than, another. Abandoning (the
views) he had (previously) held and not taking up (another), he does
not seek a support even in knowledge. Among those who dispute he is
certainly not one to take sides.
He does not [have] recourse to a view
at all. In whom there is no inclination to either extreme, for
becoming or non-becoming, here or in another existence, for him there
does not exist a fixed viewpoint on investigating the doctrines
assumed (by others). Concerning the seen, the heard and the cognized
he does not form the least notion.
That brahman (i.e. a perfected one)
who does not grasp at a view, with what could he be identified in the
world?
"They do not speculate nor pursue (any notion); doctrines are not accepted by them. A (true) brahmana is beyond, does not fall back on
views."
Snp 4.5
I have asked your questions in a different way before. I asked: Why the view “I am the owner of my karma” not contradict anatta?
The best answer for this question, by Sankha Kulathantille, has answered it very well.
Anatta is at the level of ultimate reality. That is for advanced
practitioners of Buddhism. Trying to teach Anatta to everyone
regardless of their mental maturity will not be productive as many
will end up being more confused than they already are. That's why there
are teachings in Buddhism that help you develop the mind at a
conceptual level where you are familiar and comfortable. It is
important not to mix up these teachings with the teachings of ultimate
reality.
That means views like "I am the owner of my karma" and rebirth are simply used as skillful means, as crutches to help one who hasn't overcome the fetter of self-view (sakkaya ditthi) and who hasn't understood anatta yet.