Speaking from father's perspective rather than UX designer (well, combining it a little bit) I think it is great for educative toys to keep children focused on a particular activity, which is playing with the toy. The thing is that children at the age of 0-2 years often lose their attention atracted by some sounds around, other toys etc.
In the same time it is good to keep them focused on something because:
- in case of educative toys: they will keep playing with them, expanding their understanding of how to interact in general with world around and the toy, which is the goal of the toy
- being focused itself is a skill as well. Skipping from one play to another is therefore noneducative, and playing a focus sound is something that prevents it
- last, yet not least: in many cases parents want children to be focused on something just to give them (parents) some breath
One of the greatest toys my both daughters used to love was this one: http://www.fisher-price.com/en_Us/products/30407
The toy used to play a sound after a period of inactivity. It was a bare "Goodbye", but many times I have seen my daughters coming back to the play.
I think that the question is a little bit different: is the sound annoying or not. In case of the toy I have mentioned, it was totally not annoying, it just grabbed the attention in a very nice, polite way - the toy just communicated that it wants to say goodbye if the user does not want to play with it any more. Yet, the result was usually quite different.
Regarding washing machines and other home appliances, the annoyance comes from the chore the sound communicates. You need to take out the laundry, so it basically says "Hey, I need you to take care of me." There is quite a difference between telling someone that he has to do something and kindly coughing in the corner saying "I'm here, goodbye for now, but if you want to play more, I am always ready."
By the way, there was another toy tat followed the same scheme, an interactive table - another great and beloved toy, however I don't remember the brand. Something tells me it was Little Tikes, but not sure about it, cannot find it on their site, maybe it's discontinued or I am wrong regarding the brand.