But Britain and the Netherlands never had the same king. William III of Orange was not king of the Netherlands: he was 'stadtholder' of several Dutch provinces and Captain-General of the Dutch army. To explain what this means, I'll have to take a step back and explain how the Netherlands were organised at that time.

Background

The country of the Netherlands in this time is called 'The Dutch Republic', short for 'Republic of the United Netherlands' (Republiek der Verenigde Nederlanden). The Dutch Republic consisted of 8 provinces which were part of a larger group of 17 provinces (spanning The Netherlands, Belgium, Luxembourg, and extreme northern France) collectively called 'The Netherlands'. These provinces were not a single country but each province did have the same ruler, which in the second half of the 16th century was Philip II, who was also king of Spain. In the 1560s large parts of the 17 provinces revolted against Philip II. After a tumultuous period of a couple of decades the northernmost 8 provinces emerged as independent (effectively, official recognition had to wait a while longer), whereas the other provinces remained with Philip II.

At first these northern provinces looked for a new ruler to govern them, but after a couple of failed attempts to get someone for the job they decided to become a republic. Each province governed itself through a representative body called the States (Staten). The States included representatives from the nobility and the cities. These States held the power in the provinces, but it would be nice to have a single person to take care of certain executive things, such as maintaining peace and order. This person was the stadtholder of the province. (A stadtholder originally was someone who temporarily took care of things in absence of the ruler; 'stadt' being related to the word 'instead'. The Dutch took this office and made it a permanent appointment by the States instead of a temporary one by the - no longer existing - ruler). Usually several provinces would choose the same stadtholder: the Prince of Orange.

So each province had States (representatives) and a stadtholder (executive). That's fine for governing the provinces, but they had to figure something out for the country as a whole. The Dutch Republic as a whole was governed by the States-General, which was a body consisting of representatives of the States of 7 of the 8 provinces (one province, Drenthe, had misbehaved during the war and was too poor to be of any consequence, so they were ignored). The States-General decided on all matters involving foreign affairs and defence. Other matters (including sovereignty) remained with the provinces. To make the defence effective, the States-General appointed a single person to command the army as Captain-General. Usually the stadtholder of Holland (the most important province) was appointed Captain-General.

William III

William III of Orange was the son of William II, who was not only stadtholder of all but one province but also the son in law of Charles I of England. When William II died, William III was still unborn. 5 provinces decided not to appoint a replacement and went without a stadtholder for a couple of decades. In 1672 though they were forced to come back on their decision. The Republic was attacked from all sides by English, French and German (Munster) forces. A strong leader was needed to avoid complete destruction of the Republic, so the States-General appointed William III as Captain-General. Shortly thereafter the 5 provinces without stadtholder appointed him as stadtholder. William III led the Dutch Republic back from the brink of destruction.

His successful defence of the country made William III very popular and as stadtholder of 5 provinces and Captain-General he was the most influential politician of the Republic, but he still was just a politician in a republic. He was not a sovereign ruler, as a king would be. William III married Mary, daughter of (later) James II of England. His (and his father's) ties to English royalty led to the Glorious Revolution which made him king of England (etc.). Until his death in 1702 William III would remain both king of England and stadtholder in the Dutch Republic.

An answer!

The answer to your question "why were Britain and the Netherlands never formally combined into one country if they had the same king" thus is that they did not have the same king and that the Dutch provinces were sovereign entities which governed themselves (partly collectively). So there was nothing to combine. William III was a 'public servant' of the Dutch provinces who became king of England.

Unfortunately I don't know enough about the 1708 interregnum crisis to say what was or was not (and why) considered.

(edits for spelling)