They were AFAIK. However, while William of Gloucester is often touted as a "great hope" the truth is that he'd possibly end up as a sort of British Carlos II. He suffered from asthma (Kensington House was bought because it was believed the air from the nearby gravel pits would be beneficial), hydrocephaly (the autopsy drained a cup of water from his brain), and chronic spells of dizzyness (which led to his reluctance to climb stairs and him having to be tied to the saddle of a horse when learning to ride). Likely this was also the reason why he was late learning to walk. Not necessarily stupidity or disability but a subconscious fear of falling
It is thought that the hydrocephaly stemmed from a case of meningitis he suffered from as an infant. The dizziness he had is also thought to be because of the hydrocephaly, so if his meningitis never happened his health would not be much worse than that of his father or uncle William, who both also suffered from asthma. With only the asthma I see no reason as to why he shouldn’t have been able to grow up and potentially have descendants of his own.
@Ivan Lupo I was under the impression Anne caught syphilis from her hubby was an explanation for the frequent child losing
Syphilis has often been used as a go-to disease when there have been health issues among nobility involving instability or infertility, but I think it very unlikely here. George and Anne’s marriage was noted as being particularly faithful, and as far as I know he had no known mistresses. It is far more likely that Anne suffered from antiphospholid syndrome or lupus, of which I consider the former more likely, as I don’t believe there are sources describing the butterflyrash common to lupus on her.
Were the early two daughters reasonably healthy? Because then them being taken out by smallpox is pure bad luck, and has nothing to do with Anne's likely underlying health issues.
Afaik the two daughters were healthy enough and only died due to smallpox, but they were so young when they died so it’s hard to tell, really.
As a wife for Prince William, then how about Marie-Louise of Hesse-Kassel or Caroline of Ansbach? Both come from decent protestant families and are not closely related to the royal family. They both also were fertile otl, so childbearing should not be an issue. They also had some intelligence. Of the two, Marie-Louise would be closer in age, but if they wanted William producing heirs asap, then Caroline would maybe be the likelier choice.