Why does the speaker identify so intensely with the wind?

The speaker, who we can interpret as Shelley himself, wants to be like the west wind. He interprets the power of the wind as a metaphor for poetic inspiration and as a catalyst of social change. This idea of the wind inspiring and powering flight lends itself to ideas of being uplifted:

If I were a dead leaf thou mightest bear;
If I were a swift cloud to fly with thee...

He wants to be lifted to new poetic heights. And in terms of Shelley's ideas about social change, he wants to see a powerful movement. He hopes that his poetry, like the power of the west wind, might power a social change and/or movement.

The final stanza really sums up these ideas. He is literally saying to the wind, "be me." Just as the wind scatters leaves and seeds all over the world to go into the ground and be born again, Shelley wants his own poetry to be scattered all over the world in the hopes that his lines might grow, inspire, and uplift those who read them:

Be thou, Spirit fierce,
My spirit! Be thou me, impetuous one! Drive my dead thoughts over the universe
Like withered leaves to quicken a new birth!
And, by the incantation of this verse, Scatter, as from an unextinguished hearth
Ashes and sparks, my words among mankind!