Why is Lakshmana not considered an incarnation of Vishnu?

Question

According to the Mahabharata, Balarama is mentioned to be an incarnation of Adi-Shesha-Naga:

And Baladeva of exceeding strength was a portion of the Naga, Shesha. (Mahabharata 1.61.91)

On the hand, the third chapter of the first canto of the Srimad Bhagavatam states Balarama to be an incarnation of Vishnu:

In the nineteenth and twentieth incarnations, the Lord advented Himself as Lord Balarama and Lord Krsna in the family of Vrsni [the Yadu dynasty], and by so doing He removed the burden of the world. (Srimad Bhagavatam 1.3.23)

The two "contradictory" verses are reconciled by the Srimad Bhagavatam itself in the second chapter of the tenth canto of the Srimad Bhagavatam:

When Kamsa had killed six of the children born from Devakî, the seventh one, a plenary expansion of Vishnu who was celebrated with the name Ananta, therefore [was born] as an embryo in the womb of Devakî ... [Vishnu] instructed His spiritual potency [Yoga-mâyâ] as follows: ... "In the womb of Devakî there is the embryo known as [Ananta-]S'esha who is a plenary expansion of Me. Take care of a smooth transition from her womb to the womb of Rohinî.... Because He changes wombs [from Devakī to the womb of Rohinī] the people of the world will address Him with the name Sankarshana, because He brings pleasure to the people [of Gokula] He will be called Râma and because of His great physical strength He will be named Balabhadra."

Thus, Balarama can be regarded aa an incarnation of Vishnu. Similarly, many Sri Vaishnavas who claim Ramanujacharya as an incarnation of Adi-Shesha-Naga at times, call Him an incarnation of Vishnu. So if Ramanujacharya and Balarama can be considered incarnations of Vishnu since Adi-Shesha-Naga is simply an expansion of Vishnu Himself, why is Lakshmana, who is also considered as an incarnation of Adi-Shesha-Naga, not called as an incarnation of Vishnu?

Answer 1

In Valmiki Ramayanam BalaKanda it is mentioned that all the 4 sons born for Dasaratha are incarnations of Vishnu in various proportions.

अथ लक्ष्मणशत्रुघ्नौ सुमित्राऽजनयत्सुतौ।।1.18.13।।
वीरौसर्वास्त्रकुशलौ विष्णोरर्धसमन्वितौ।

One fourth of Vishnu manifest. Sumitrá too a noble pair, Called Lakshman and S'atrughna, bare, Of high emprise, devoted, true, Sharers in Vishnu's essence too.

The above text is relevant for Lakshmana's birth and it is clear that he is considered incarnation of Vishnu.

chapter 19, Bala Kanda of Ramayana

In Srimad Bhagavatam, Skanda 9 Chapter 10, it is mentioned that all four sons of Dasharatha are incarnations of Lord Vishnu.

Thanks to @SwiftPushkar for giving the Bhagavatam reference.

Answer 2

Lakshmana is considered a portion of Vishnu in Valmiki Ramayana.

When Ravan entered the battlefield against Rama for the very first time. Ravan hurled Brahma weapon twice upon Lakshmana and Lakshmana absorbed the divine weapon.

स तान् प्रचिच्चेद हि राक्षस इन्द्रश् | चित्त्वा च ताम्ल् लक्ष्मणम् आजघान | शरेण काल अग्नि सम प्रभेण | स्वयम्भु दत्तेन ललाट देशे || ६-५९-१०४

Whereupon, Ravana the King of Demons shattered those pointed arrows and struck Lakshmana in the forehead with a struck Lakshmana in the forehead with a shaft as bright as the Fire of Time, which had been bestowed on him by Brahma the Lord of Creation.

Then Ravan used the divine spear of Lord Brahma on Laksmana.

स कृत्त चापह् शर ताडितश् च | स्वेद आर्द्र गात्रो रुधिर अवसिक्तह् | जग्राह शक्तिम् समुदग्र शक्तिह् | स्वयम्भु दत्ताम् युधि देव शत्रुह् || ६-५९-१०७

Ravana, the enemy of celestials, whose bow was broken, struck by the arrows, his limbs spattered with flesh, and streaming with blood, himself of formidable energy, seized in the battle a spear gifted to him by Brahma the Lord of Creation.

शक्त्याब्राह्म्या तु सौमित्रिस्ताडितोऽपि स्तनान्तरे | विष्णोरमीमांस्यभागमात्मानं प्रत्यनुस्मरत् || ६-५९-११२

Lakshmana, though wounded in the breast by Brahma's weapon, recollected that he was an inconceivable fraction of Vishnu Himself.

Yuddha Kanda Sarga 59