Again, my
sensus catholicus tells me that the penitent would need to confess at least any mortal sins, if they survive the illness that occasioned the AOTS in the first place, similar to the way one must confess mortal sins that they forgot to confess in a prior reception of the sacrament of penance.
My source* informs me that if the individual is unable to make confession that Anointing of the Sick absolves one from their mortal sins. It says nothing about going to confession should one sufficiently recover to do so. However, I can understand the point you're making and I may do some more research on this.
*Joesph, P. (2009) Archbishop Michael Sheehans' Apologetics and Catholic Doctrine, 6th/4th Edition. London: Baronius Press Ltd (ISBN-13: 9781905574452)
I checked McHugh and Callan, and they don't say anything about confession of mortal sins if one survives the illness. Here is what they do say:
(f) The effects of Extreme Unction are _per se_ an increase of
sanctifying grace, since this is a Sacrament of the Living; _per
accidens_ (i.e., when the recipient is not in the state of grace, but
is in good faith and has attrition) the forgiveness of sins and first
grace. Extreme Unction produces first grace more surely than does
absolution, if the penitent is unconscious, since it does not call for
any external manifestation of contrition; hence the importance of
anointing those who are dying but unconscious. The special benefit of
Extreme Unction is immediate preparation of the soul for entrance to
heaven, though restoration of the health of the body is sometimes
vouchsafed when this is for the spiritual good of the sick person.
Venial sins and the remains of past sins (i.e., the debility left by
them) are removed and the soul is strengthened with confidence as to
things past and future and with peace and resignation as to present
suffering. Since the Sacrament is given for the period of danger of
death, it cannot be repeated during the same danger; but should the
patient recover and relapse into a distinct danger through the same or
another sickness, there arises a new need and the Sacrament may then be
repeated.
2775. Special Duties.--In addition to the duties that are common in all
the Sacraments, the following duties should be noted in reference to
Extreme Unction.
(a) The Recipient.--_Per se_, Extreme Unction is not necessary as a
means to salvation, for sanctifying grace may be had or recovered
without it; but _per accidens_ it would be necessary as a means, if a
dying person were in mortal sin and could not recover grace except
through it. He who omits Extreme Unction unwillingly or for a good
reason (e.g., because he is well prepared for death and cannot get a
priest without very grave inconvenience) does not sin. He who omits the
Sacrament voluntarily and without good reason, is guilty of grave sin
if he acts from contempt, or gives scandal, or exposes himself to
eternal damnation; but if there is no contempt, scandal or danger to
salvation, sin is indeed committed by the neglect at such a crisis of
so important a spiritual aid, but only venial sin, since there is no
grave precept to receive this Sacrament. The recipient of Extreme
Unction should be in the state of grace; and hence, if he has mortal
sin on his conscience, he must beforehand make an act of contrition or
receive absolution with attrition, or, if neither is possible, he must
make an act of attrition. The custom of the Church calls for confession
before Extreme Unction, and divine law commands confession if one is in
mortal sin and in danger of death.
And there's also this:
The rule about the old is that those who have reached sixty years and show some signs of approaching death, such as great feebleness or fainting spells, even though they have no special malady, may be anointed; for their old age itself is a disease.Good to know, said this sexagenarian.