To give a short answer: stability and power.

Consider that at the outbreak of the Thirty Years War, the electoral college was divided in three: there were the three Archbishops, the Lutheran elector of Saxony, the Calvinist electors in Brandenburg and the Palatinate, and the King of Bohemia--who was also the Archduke of Austria. The interesting thing about the HRE pre-Thirty Years War is that there was a strong moderate party among the Protestants who did not want to force a crisis with their Catholic Emperor, the leader of which was Saxony. On the other hand, there were the more radical ones, such as Frederick V, the Elector Palatine who did want to see a Protestant elected to the Imperial throne, despite the crisis that might bring. The various German princes benefited heavily from stability, and--so long as the new Habsburg Emperor was willing to confirm their rights and privileges--would be willing to cast their vote for him, and vote him funds necessary to defend the Empire against external threats, like the Turks and French. It often seemed that the Lutherans were more worried about their fellow Protestants--the Calvinists--provoking a crisis and upsetting the balance and stability of the Empire.

When Frederick V accepted the Bohemian throne, even his own Evangelical Union was unwilling to help him. The Protestant elector of Saxony, John George, even helped lead the forces that expelled Frederick from the Bohemian throne, and restore Ferdinand II to his Bohemian lands. The hope was--of course--that by standing with the Emperor--they would be in a position to ensure that the Emperor would respect them, and their rights and privileges. While individual Emperors may not have been well liked, the office of Emperor was quite respected, and there was a strong taboo with regard to rebellion against your rightful sovereign. As such, the tool to be used to redress issues with the Emperor was in the Diet or other assembly, rather than to openly defy him.

In addition, more practically, the Habsburg Archduke of Austria was simply the most individually powerful German prince, ruling as he did the Kingdom of Boehmia, the Archduchy of Austria, and what parts of Hungary remained free from the Turks. Combining his Austrian, Bohemian, and Hungarian lands gave him significantly more territory, population, and wealth than other German princes. Since the Emperor was expected to defend the Empire against external threats, and thus to pay for these wars from his own revenue, it was common sense that a powerful prince should be elected Emperor. While the princes and estates were willing to vote the Emperor taxes and income to assist him in his task, the Emperor was still expected to foot the majority of the bill.

Later on--espescially as we get more into the 18th century--we see a trend of Imperial princes seeking an external royal title. The Dukes of Saxony became the Kings of Poland, and the Margrave of Brandenburg was granted the title King in Prussia. While I've studied this era less than the early modern and the pre-Thirty Years War Holy Roman Empire, it seems to me that this implies that--rather than rebel against the Emperor--the princes who sought greater autonomy attempted to achieve it by acquiring royal title outside of the Empire. In this sense, they could avoid confrontation with the Habsburg Emperor, while also achieving their own independent sovereign title.

Hopefully this helps answer your question, and feel free to ask any follow ups!