Why is it that the cornea of the eye has no capillaries?

Because it gains its oxygen directly from the air. Otherwise blood vessels would obscure the vision. But if you wear soft contact lenses too much veins can grow to supply the oxygen being prevented from reaching the eye and cause serious vision problems.

https://www.oxygenworldwide.com/news/articles-and-information/635-your-eyes-and-oxygen.html

The above explanation does not quite present the full picture:

The only two tissues in the human body that do not need a blood supply are corneas and cartilage. The cornea cannot have a blood supply ie capillaries as this will decrease transparency which is the one attribute the cornea must have. To ensure there is no blood supply, the outer layer of the cornea, the transparent epithelium secretes, via the aqueous humour a protein VEGFR-3 (vascular endothelial growth factor receptor-3). VEGFR-3 halts angiogenesis (blood vessel growth) by acting as a "sink" to bind or neutralize the growth factors sent by the body to stimulate the growth of blood vessels. This keeps the blood vessel clear.
In the example presented above, the soft contact lens forms a seal with the outer cornea thereby reducing the amount of VEGFR-3 that can be secreted
As the cornea has no blood supply, it needs to find its nutrients from other sources. Instead, the cornea receives its nourishment from the tears that lubricate the cornea and aqueous humor (a fluid in the anterior portion of the eye) that fills the chamber behind it.

http://www.kumc.edu/Documents/ophthalmology/Cornea%20Structure%20Layers%20and%20Function%20web.pdf
https://www.pnas.org/content/104/13/5413
https://www.eurekalert.org/pub_releases/2006-07/seri-sdw071406.php