Yes refurbished phones offer all the features. there is no harm in buying them. In fact, it is an eco friendly way to use a smartphone and you can save money too. They come at a cheap price.
The only real concern is if you're buying old-stock refurbished. With today's locked-in batteries, any older phone is something of a gamble. But there should be no concern over buying a present-year refurbished phone from a reputable company.