When Alsace-Lorraine was annexed, it was an option to make it a province of Prussia, but there also was the option to make it a part of Bavaria or to make it a new state under direct administration of the Emperor. What we need to understand is that Germany after 1866 was dominated by Prussia, and most crucial political decisions made regarding the future of Alsace-Lorraine were made by Prussians, like Chancellor Bismarck. Let's keep that in mind, but first, we need to dig deeper.

During the Enlightenment, and after the French Revolution in particular, several European states had to find a solution for the Kulturkampf, that is the fact that the new emerging nation states claimed territory and competences that once belonged to the Papal States and the Catholic Church, like education and welfare. This led to the question if and how state and church should be separated. France established a state-run church, while Italy solved the conflict very late, in the 1920s, after Mussolini accepted Vatican City as Papal State, and guaranteed protection. When Italian nationalists tried to establish a nationstate in Rome in 1849, France and Spain intervened on side of the Papal State, so the attempt failed. France couldn't intervene again in 1870/71 since French troops were needed to fight the German states, which led to the Italian unification (last phase of Risorgimento).

Germany, however, was (and still is) separated in a part that's mostly catholic (the southern and western parts of it, with states like Bavaria and Saxony) and a part that is mostly protestant (in the northern and eastern parts, including Prussia). There were many tensions between catholics and protestants which, on several occasions, went violent, and made diplomacy between catholic and protestant states of the Empire a cultural battlefield. Like in neighboring countries, German monarchs had seized papal property to enlarge their territories and population, which led to a part of catholic population to oppose the nation states they became citizens of. Chancellor Bismarck considered them as enemy of the state, because they endangered the unity of the very young and, yet, unstable Empire. When Prussia became the dominant state in Germany after 1813, protestant culture also became dominant in the Empire, which led to a more anti-papal, sometimes anti-catholic stance nationwide.

Another factor to consider was the allocation of political and military power in the Empire. When the Holy Roman Empire ceased to exist in 1806, there was the question how a reunified Germany would look like: Some states - Prussia in particular - preferred a "small" (kleindeutsch) solution, that is, Germany minus Austria, while the states in southern Germany, like Bavaria, preferred the "big" solution (großdeutsch), that is, Germany including Austria. In the German war of 1866, Austria (which was part of the German Federation back then) fought Prussia over the question who would be the major power controlling other German states, and Prussia was victorious. After the war, the southern German states preferred the "big" solution to have Austria (which was mostly catholic, by the way) as a major power to counterweight Prussian dominance, on a cultural, military, political, and also religious level.

Alsace-Lorraine had a population that was mostly catholic, so making it a province of Prussia would have fanned the flames of Kulturkampf in Germany - it would have meant that Prussia would apply its rules of separating state and church on the catholic population, which already organized itself in clubs and political parties to gain political power and change the course of actions regarding the Catholic Church. And it would also enrage the southern states, because the dominance of Prussia was growing fast in the past years, endangering their integrity. Making Alsace-Lorraine part of the catholic state of Bavaria, on the other hand, might have enraged protestants and was not part of Prussian interest, because it would have shift political power in the Empire - Bavaria was, after Prussia, the German state with the biggest population (approx. 5.8 million, while Alsace-Lorraine had 1.5 million).

Prussia's main interest was to keep inner peace, while keeping the other states small to control them with ease. Therefore, and to keep religious peace, it considered unifying Germany under Prussian dominance, by making Alsace-Lorraine a state of its own. Austria, after it had lost the war in 1866, had already drifted away from the other German states and created the Dual Monarchy with Hungary to strengthen its position against neighboring powers. The states of southern Germany, without Austria's support, had no other choice than join the Prussian-dominated North German Federation to survive between the major powers France, Italy, Prussia and Austria, and therefore, the unification of the Empire was concluded.