Why KL Divergence instead of Cross-entropy in VAE
Answering with some theoretical understanding  of Variational auto-encoders.
In the general architecture of encoders and decoders, the encoder encodes the input a latent-space, and the decoder reconstructs the input from the encoded latent space.
However, the Variational auto-encoders (VAE), the input is encoded to a latent-distribution instead of a point in a latent space. This latent distribution is considered to be Normal Gaussian distribution (Which can be expressed in terms of mean and variance). Further, decoders samples a point in this distribution and reconstructs the input. Since, VAE encoder encodes to a distribution than a point in a latent space, and KL divergence is use to measure the difference between the distribution, it is used as a regularization term in the loss function.