Yes, it happens sometimes that the intended place to stop is full. Try being a trucker - that's even worse.
Reading the posts and traveling the country, there are a wide variety of types of rest areas. Some are elaborate - often called an Oasis (from memory), with gas, restaurants, etc. in addition to the usual restroom facilities. Other places are the basic toilets, a few vending machines, and usually a few places to sit and eat.
It comes down to a couple of things - mainly does that particular state feel a need to spend money on rest area facilities or not? I've been in some nice ones and others that I couldn't get out of fast enough. Sometimes in the same state.
Every year, there is debate in our legislature on this issue whenever money for rest areas is discussed. Some claim the state should just get out of the business all together and let private business do everything (I will note none of our rest areas have restaurants or gas and diesel sales). Others claim it is a driver safety issue. I tend to think a mixture of the two works well - they both have their place.