Já pensou que você poderia querer comprar uma casa e um carro? Sim?
I want to buy a car and house.
E que tal se você tem o dinheiro suficiente e tem a possibilidade de comprar dois itens ao mesmo tempo?
I want to buy both a car and a house. (instead of both a car and plot -OR- ...both a car and a boat.)
I want to buy a car and house doesn´t necessarily mean that you want to buy them at the same time (now, for instance).
So, sometimes to avoid ambiguity, you could use "both" as illustrated by the given examples.
Of course, sometimes they could be interchangeable, perhaps even in the above example, but if you can avoid ambiguity to your reader, then why not to spare him the headache?
"I want to buy a car and a house" could be something to be done in the future, to be partially done now, etc. To my thinking "both" brings a certain "at the same time" component to it. Not necessarily, but it points in that direction, more often than not.