Parinibbana is a state where the five khandhas cease to exist. If rupa, vedana, sanna, sankhara and vinnana cease to exist, what kind of happiness is sensed, felt, perceived, thought of or otherwise experienced?
Yet Parinibbana is a blissful state, far more blissful than any state that can be sensed, felt, perceived, thought of or otherwise experienced by the five khandhas.
To me, I think The Buddha would fully agree that bliss and sukha could refer merely to the permanent cessation of dukkha, without any pleasant vedana, piti or other ecstatic or happy sensation associated with it. Therefore it is not necessary for any Self to experience it.
In the Pañcakanga Sutta SN 36.19, The Buddha stated that a bhikkhu going totally beyond the dimension of neither perception nor non-perception, enters and remains in the cessation of perception and feeling. This is a pleasure that is finer than what is experienced by someone meditating in the dimension of neither perception nor non-perception.
If I am correct, the state of cessation of perception and feeling is only achieved by Arahants who attain Nibbana by cultivating the highest jhana.
The Buddha also stated that ‘…when He describes what’s included in happiness, he’s not just referring to pleasant feeling. The Realized One describes pleasure as included in happiness wherever it’s found, and in whatever context.’ Hence even when vedana and sanna cease, it is possible to experience sukha.
Nibbana Sutta: Unbinding AN 9.34 also states how extinguishment of defilements and afflictions is bliss.
Therefore, by simply having no dukkha in it, Nibbana is sukha, and this sukha surpasses any sukha that can be experienced in this world, even that of sense pleasures or the highest, most sublime jhanic bliss. Furthermore, this will be permanent.
We can compare Nibbana to sleep, although Nibbana is much, much more blissful than sleep. When a being is severely fatigued, sleepy and in need of rest, possibly the greatest happiness it can achieve is not from sensual pleasures, or even from jhanic absorption and bliss, but from a deep, restful, much needed sleep.
We are like the severely tired, and sleep-deprived beings on this sansaric journey, yet we have become obsessed with sense pleasures that further add to our burden and sleepiness, or we become obsessed with becoming this or that or, being averse to this or that.
All these add to our sleepiness, but we fear to sleep, because we are afraid to give up our obsessions with sense pleasures, or desires to become this or that, or not to become this or that. We are also afraid that we will never wake up from our sleep to again experience all those burdens that we mistakenly think of as happiness.
Yet, when we sleep, our minds are still not fully at rest. There is sankhara associated with breathing and the beating of our hearts and so on. However, in Nibbana, there is no sankhara and it is truly peaceful and happy indeed.
I hope this helps. I got the idea of comparing sleep to Nibbana from Lal, and have found it very helpful and beneficial. Thank you very much for teaching the Dhamma to me and all other beings, Lal!