Well, because Lord Vishnu couldn't. Please don't barge in with lectures, this is a sectarian belief and substantiated with Evidence.
The question was framed as well as answered by the Sacred Tirumurai of the Shaiva Siddhanta philosophy. The Sacred Tamil Tirumurai are known as the Tamil Veda, whose authority is Equal to the Vedas themselves.
Sage Manikkavaçakar says,
Obj: He ate halāhalam from the sounding Sea, that day arisen with mighty din; what means this wondrous act my dear?
Ans: Had he not eaten on that day the poison fierce, Ayan and Māl and all the other Gods of upper heaven had died, behold, cāralō
~ Tiruvāçagam Hymn XII.VIII
Ayan is Brahma and Māl is Vishnu.
Brahma himself agrees to this fact, the Brahmand Purana says,
Devas said,
Janardana of reddish white body has been rendered black on being scorched by that poison whose lustre is on par with the dark fire of ultimate destruction. On seeing Janardana Of reddish white limbs rendered black by its burning, all of us have become frightened and we sought refuge in you alone
~ Brahmanda Purana 1.2.25.54–59a
Brahma replies,
O Devas, sages and ascetics, listen all of you. The poison that has the lustre of the dark fire of destruction and what we all know as Kālakūta has appeared while the great ocean was being churned. Immediately by its very appearance Devas lost all lustre and they did not shine the moment it cropped up. Neither Vishnu, nor I nor the leading Devas can bear the burn of its attack except Shankara
~ Brahmanda Purana 59b-63
The Vayu Purana says along similar lines
Neither Vishnu, nor I nor the leading Devas can bear the burn of that poison except Siva
~ Vayu Purana 1.54.63
Hara alone is capable of swallowing the poison. Hope that is clear.
The Skanda Purana says,
Highly terrible poison Kālakūṭa with flaming sparks around was born of the Milk Ocean, due to the churning with Manḍara. No one other than Maheśa could endure it. On account of its flames, Viṣṇu turned back.
~ Skanda Purana Kashi Kanda 95.57
The Agamas say as well,
Victory! Remover of the power of the Kalakuta Poison, Which spoilt the body of Vishnu
~ Kirana Agama Vidya Pada 1.4
The texts which ascribe that it wasn't Siva but Vishnu through Whom and by whose grace, Siva drank the poison, is rejected owing to the contradiction with the Agamas. So Puranas don't hold authority over Agamas.
Umapati Sivacarya beautifully summarizes this in his prologue of Sankarpa Nirakaranam,
He is the Supreme Being (antamil kadavul) that took for Himself the poison that emanated when the Devas and the Asuras churned the ocean and gave them the assurance that as He is the source of all good, evil will have no force
~ Sankarpa Nirakaranam Verse 2
Note: I shall make a separate post about Keshi Suktam and other Pauranik texts in this regard. The Keshi Suktam is very often misunderstood as conveying a meaning which is antagonistic to its original intent.
