Why don't we realise space instead of Nibbana?

the difference between aggregate existent, nibbāna existent, and nonexistent (paññatti):

Nibbāna has no cause, because nibbāna never arise (every aggregate arisen by causes). Nibbāna is reality, existent, because nibbāna is the end of suffering (5 aggregates), the opposite side of suffering.

But paññatti, such as space, is not reality, not existent, although we can know it. Because paññatti has not any cause, too. And mainly, it is neither included in aggregate existent, nor included in nibbāna existent. It is not arises by causes like aggregate, and not opposite side of suffering like nibbāna. Paññatti is imagination that is imagined by consciousness. So we can imagine paññatti follow to aggregate, nibbāna, paññatti, or not follow to anything (=wrong view). That magination of consciousness never arise, but aggregate can arise even though without imagine. We can not called "is made by" because paññatti never is made by causes. It is just imagination.

So, arahanta-phalasamāpatti is difference of paññatti, because arahanta-phalasamāpatti completely abadon evey akusala, before arahanta can realise nibbāna. But everyone can realise, imagine, paññatti.

For more information of space paññatti, see ChrisW's answer.

To the ignorant eye, space is space. Looking at space with wisdom, one sees Nibanna.

Space is not space. It is neither infinite, nor finite, nor both, nor any combination of these. There is no length nor height nor width nor distance nor closeness nor solidity nor empty space. Space is not space as we know it. All points in space are one single point and this one single point is all points in space.

To the ignorant eye, object is object. Looking at object with wisdom, one sees Nibanna.

Object is not object. It is neither infinite, nor finite, nor both, nor any combination of these. There is no length nor height nor width nor distance nor closeness nor solidity nor empty space. Object is not object as we know it. All objects are one single object and this one single object is all objects.

Everything is Nibanna.

Clouded with ignorance, space is the closest we can get to Nibanna with our senses.

Once ignorance is removed, Nibanna can be reached.

Space is not unconditioned. Space is simply a derived element. In other words, it's merely the absence of matter. When matter arise, space perish, when matter perish, space arise.

Space does not exist independently of kamma & cause. By kamma (action), space can be filled, such as filling a hole with soil. Or by cause, space can be created or removed, such as a volcanic eruption creating a cave with space but filling space in a crevice. Or when sickness blocks the space in the nostril.

The Lord Buddha said the realisation of space is conditioned & not Nibbana.

Nibbana is dispassion; Nibbana is non-attachment; Nibbana is the destruction of craving; Nibbana is the absence of greed, hatred & delusion. Therefore, a mind abiding in Nibbana can walk & talk. Where as a mind abiding in space cannot walk or talk. That is why the Buddha rejected the dimension of the infinitude of space as Nibbana; because the dimension of the infinitude of space is limited, bondage, conditioned & not freedom.

One discerns that 'If I were to direct equanimity as pure & bright as this towards the dimension of the infinitude of space and to develop the mind along those lines, that would be fabricated'. MN 140

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And what is the space property?... Anything... that is space, spatial... the holes of the ears, the nostrils, the mouth, the [passage] whereby what is eaten, drunk, consumed & tasted gets swallowed, and where it collects... MN 62

In the course of the future there will be monks who won't listen when discourses that are words of the Tathagata — deep, deep in their meaning, transcendent, connected with emptiness — are being recited. They won't lend ear, won't set their hearts on knowing them, won't regard these teachings as worth grasping or mastering. But they will listen when discourses that are literary works — the works of poets, elegant in sound, elegant in rhetoric, the work of outsiders, words of disciples — are recited. They will lend ear and set their hearts on knowing them. They will regard these teachings as worth grasping & mastering. In this way the disappearance of the discourses that are words of the Tathagata — deep, deep in their meaning, transcendent, connected with emptiness — will come about. SN 20.7

What do you mean by "realize"? See the definition of Ākāsa here, which begins,

'space', is, according to Com., of two kinds:

1. limited space (paricchinnākāsa or paricchedākāsa),
2. endless space (anantākāsa), i.e. cosmic space.

1) Limited space, under the name of ākāsa-dhātu (space element), belongs to derived corporeality (s. khandha, Summary I; Dhs 638) and to a six fold classification of elements (s. dhātu; M.112, M.115, M.140). It is also an object of kasina meditation. It is defined as follows: "The space element has the characteristic of delimiting matter. Its function is to indicate the boundaries of matter. It is manifested as the confines of matter; or its manifestation consists in being untouched (by the 4 great elements), and in holes and apertures. Its proximate cause is the matter delimited. It is on account of the space element that one can say of material things delimited that 'this is above. below, around that' " (Vis.M. XIV.63).

2) Endless space is called in Atthasālini ajatākāsa, 'unentangled', i.e. unobstructed or empty space. It is the object of the first immaterial absorption (s. jhāna), the sphere of boundless space (ākāsānañcāyatana). According to Abhidhamma philosophy, endless space has no objective reality (being purely conceptual), which is indicated by the fact that it is not included in the triad of the wholesome (kusalatika), which comprises the entire reality. Later Buddhist schools have regarded it as one of several unconditioned or uncreated states (asankhata dharma) - a view that is rejected in Kath. (s. Guide. p. 70). Theravāda Buddhism recognizes only Nibbāna as an unconditioned element (asankhata-dhātu: s. Dhs. 1084).

So maybe people do perceive space: both limited space (in ordinary perception) and unlimited space (as an object of meditation).