Germany was unified by Prussia for a number of reasons. In terms of purely Prussian politics there are at least five causes.
First and foremost and most glaringly, the issue of giving Prussia continuous, secure, solid, land borders. Prussia's issue here were a major motivator in all its wars up to the 19th Century.
Second, Prussia had been the state keeping up the most consistent rivalry within Germany with Austria, and Austria's disasters with France and in 1848-9 were major limits on Austria's ultimate abilities to counter Prussia with prestige.
Third, Prussia had already been gobbling up little Germanies for some time, what Bismarck did was an increase in scale, not in any kind of different concept.
Fourth, Prussia had the advantages relative to other German states of powerful friends in the UK and various Russian Tsars. Without Peter III and Alexander I, Prussia dies stillborn. Empire-building is always easier when your empire favors the interests of powers who expend strength from outside, enabling the empire-builders to conserve strength within.
Fifth, German nationalism had developed into a force in its own right, and reactionary Prussia wasn't going to see the democratic variant of the 1840s resurrect itself on Bismarck's watch.
The course of German unification, however, was partly planned, partially contingent. At no point would the Tsars of Russia have saved Prussia if they understood this would lead to aggressive, land-hungry Germany on their western borders.