Why are llamas/alpacas so popular in anime?
@ChenOrihara's link seems to be correct - it's not just an anime thing, there is an overall trend in Japan that sees alpacas being included in unlikely situations.

There's even a company that leases alpacas for weddings:



Their popularity may have been triggered when the alpaca farm in Nasu was built in 1999 - bringing 200 alpacas into the country. Subsequent farms have been built also. The Nasu farm currently has >400 alpacas