When you sing in the shower, unless you have one of those waterproof radios, you are singing a Capella or without accompaniment. This can be very tricky for both singers and directors or conductors (now that delineation is a topic for another Tuesday).
There are groups such as the Nylons who have made their names based on singing without any accompaniment other than percussion (things like drums and sticks etc.). They sing in tight harmony as do Barbershop singers and this harmony, in my opinion helps the singers stay in tune.
The Nylons make it look easy in this clip but you have to pay attention to realize that there are only percussion instruments and clapping as accompaniment.
However, it can be very tricky to stay in tune when singing without accompaniment especially for amateur singers. Personally, I almost always opt for accompaniment especially for soloists and usually for choirs. Children in particular can benefit from being able to hear the sounds they want to replicate. The piano has a full range of overtones to help fill any voids in sound but also has clear tones. The pipe or even electronic organs can sound "muddy" and make singing in tune a bit trickier especially if you are trying to hear a specific part.
Chris Rowbury has a quirky but very sane view on a capella singing that merits a read. Tell me what you think. Why I don't like "a capella".