In Shakespeare's Sonnet 18, is the argument for the immortality of the loved one flawed? Why?

The concept of immortality in Shakespeare’s “Sonnet 18” is flawed. In this sonnet, the speaker immortalizes his love for the recipient of the poem, wanting to encapsulate that feeling forever. This, intrinsically, is a flawed philosophy, because it shows a devotion and dedication to the abstract concept of love or infatuation, not a dedication to the object of those desires.
It is clear in the poem that, while the speaker is infatuated with the object of his desires, he is more caught up in the feeling of love itself. This desire to capture that feeling is what leads to the fleeting nature of many relationships, because the positive emotions ebb and flow. In reality, a devotion to the individual creates a much stronger bond than the rush of emotions one experiences when falling in love.

You could argue that the argument for the immortality of the loved one is flawed because the narrator of the poem immortalizes his love for the subject of the sonnet but not the subject herself. The loveliness that the narrator finds in the subject of the poem—loveliness so overwhelming that he says his beloved is even lovelier and more temperate than a summer's day—is what the narrator wants to immortalize by writing the poem. He believes that he has captured his beloved in "eternal lines" so that she (or possibly he, depending on the gender of the beloved) will never grow old and her beauty will never fade. In fact, her loveliness will outlast that of summer.
The flaw in this argument is that the narrator has not really captured his beloved's beauty in this sonnet but instead his love for her. What he immortalizes in the sonnet is his rapture for her and his estimation of her. He has immortalized his love but not really her beauty. Instead, we know little of her beauty or the way she looks. Instead, we know only of the way the narrator feels for her, and it is this feeling that is frozen forever in the poem. The poem immortalizes his love for his beloved and not his beloved herself.