The Trinity – Brahma, Vishnu and Shiva are considered to be superior to the Devas like Indra, because the former have much bigger roles. In Shaktism, Shakti is considered to be superior to the Trinity because she is the energy of all. Thus, these hierarchies are formed due to their responsibilities and actions – dharma and karma.
In Rukmini’s case, our mythology has only talked about her identity – Rukmini being the incarnation of Laxmi, it has never highlighted any of her achievements – and for a reason – unlike the births of Sita and Ram whose objectives, besides establishing dharma, were to set examples of ideal wife, husband, mother, ruler and so on, Krishna’s role was to set examples of an ideal lover, devotee, friend, guide, guru and to give mankind the lotus-like words of Gita, and Rukmini’s role was to be his human-consort. One has to understand that this does not imply that she was inferior – it’s just that they incarnated for some specific reasons.
Now to set an example of an ideal lover and a devotee, one needs other side of the coin too, and here comes Radha, an epitome of selfless love, the love which knew no boundaries, no age, no community. It is this devotion which pulled Krishna to play his beautiful flute, and it is the same devotion which drove Radha to the Raas Leela, forgetting her own self. This love, this devotion, this karma, pure as a prayer, a silent meditation, is what makes Radha divine, this is what turns a devotee into God. Radha-Krishna have been a part of poetry, drama and folklore since time immemorial.
So the world worships Radha to celebrate the bond of love and devotion, one of the paths to realize the Truth mentioned in the Gita. Laxmi’s incarnation as Rukmini was supposed to be a silent supporter – very important but less conspicuous. And this was by their own design, their own strategy, and their master plan.
There’s no bias between Radha and Rukmini as why one is only worshipped with Krishna. There are many temples that worship Rukmini with Krishna as Rukmini-Dwarikadhish. The rasa involved is different. But both of them are the internal potency or hladini-shakti (internal potency) of Lord Krishna and they are meant to worship with Him.
Moreover, Radha and Rukmini are non-different and we find this statement in Skanda Purana confirming this:
“rukmini dvaravatyam tu radha vrndavane vane”
TRANSLATION: Rukmini is in Dwaraka what Radha is in the forest of Vrindavan.
Importance of spiritual shelter by Srimati Radha or Mother Rukmini to the Devotee:
Radha or any of the forms of the spiritual potency of Krishna makes the way for the sincere living entity who is aspiring to render devotional service to Krishna. Krishna explains sincere devotees are always under the protection of His Internal Potency (i.e. Radharani, Mother Sita or Rukmini) this in Bhagavad-Gita:
“mahātmānas tu māṁ pārtha
daivīṁ prakṛtim āśritāḥ
bhajanty ananya-manaso
jñātvā bhūtādim avyayam”
TRANSLATION: O son of Pritha, those who are not deluded, the great souls, are under the protection of the divine nature. They are fully engaged in devotional service because they know me as the Supreme Personality of Godhead, original and inexhaustible.- Bhagavad-Gita 9.13
Also, many a times devotees are attached to a certain form of Lord Krishna and they worship but this is no great issue or some bias. Some wish to worship Radha-Krishna, or Sita-Rama, Lakshmi-Narayana, Lakshmi-Nrismhadeva. But the focus should be sincere service to Lord Krishna. Krishna reciprocates with the devotee accordingly as confirmed in Purusha-Bodhini-Upanishad:
“eko devo nitya-līlānurakto
bhakta-vyāpī hṛdy antarātmā”
TRANSLATION: “The one Supreme Personality of Godhead is eternally engaged in many, many transcendental forms in relationships with His unalloyed devotees.”
In Laghu-bhagavatamrita (5.383) expounding the above fact:
“ata evā purāṇādau kecin nara-sakhātmatām
mahendrānujatāṁ kecit kecit kṣīrābdhi-śāyitām
sahasra-śīrṣatāṁ kecit kecid vaikuṇṭha-nāthatām
brūyuḥ kṛṣṇasya munayas tat-tad-vṛtty-anugāminaḥ”
“According to the intimate relationships between Sri Krishna, the primeval Lord, and His devotees, the Puranas describe Him by various names. Sometimes He is called Narayana; sometimes Upendra (Vamana), the younger brother of Indra, King of heaven; and sometimes Kshirodakashayi Vishnu. Sometimes He is called the lord of the thousand-hooded snake, Sheshnag, and sometimes the Lord of Vaikuntha.”
Rukmini is the incarnation of Goddess of Fortune, Mother Lakshmi and Radha is the origin of Mother Lakshmi and she is extremely dear to Lord Krishna. Some scriptural evidence for this:
“yatha radha priya visnos-tasyah kundam priyam tatha
sarva gopisu saivaika visnor-atyanta-vallabha”
TRANSLATION: “Just as Radha is dear to Lord Krishna, so her bathing place [Radha-kundah] is dear to Him. She alone is His most beloved of all the Gopis.” – Padma Purana
[Krishna to Arjuna]
Trai – Lokye prithvi dhanya
yatra vrindavanam puri
tatrapi gopikah partha
yatra radhabhidha mama
TRANSLATION: “O Partha, in all the three planetary systems, this earth is especially fortunate, for on earth is the town of Vrindavan. And there the Gopis are especially glorious because among them is My Srimati Radharani.” – Adi Purana
Since she is extremely dear to the Supreme Lord, whichever sincere devotee she recommends Krishna immediately accepts unconditionally.