The Holy Roman Empire (HRE) offered many things to its members, and its non-electoral princes had their own role to play within the legal structure of the Empire.

Perhaps first and foremost was external and internal security. For threats outside of the Empire, such as the French or Swedes encroaching on its borders, or the classic threat of the Turks to Christendom, the Empire was intended to provide a united front of princes under the Emperor. The Princes of the Empire had obligations to provide soldiers for the defence of the Empire in general. Declarations of Reichskrieg--I'm sorry, I just love that term--could thus meet an externtal threat, and allow even the smallest Imperial prince to rely on the protection of the Emperor and the Empire as a whole if they came under threat from an external power. Of course, the effectiveness of this system is up for debate.

Even within the Empire, security was an important role. The Reichsreform resulted in the declaration of the 'Public Peace'. Essentially, this system was meant to outlaw the use of force to settle disputes within the Empire, and require princes to settle their disputes through a legal process--much like most modern states require their citizens. The Imperial Circles were drawn up to promote and enforce the Public Peace, and the Imperial Aulic Council (Reichshofrat) was established to serve as a supreme judicial body for settlement of disputes between the princes. This, of course, was meant to promote stability and security within the Empire, by preventing the princes from resorting to force of arms--justified by claims of right to revenge/vendetta--and binding them to basically go through an arbitration process.

So, as we can see, there was certainly a benefit to being a member of the Empire, rather than just being a random prince of a small polity in the heart of the Europe, without the protection of the Empire. The Empire provided security against external threats, by ensuring that the Empire could provide forces to the Emperor for their own defence, and security internally, by binding the princes into a legal structure to resolve their disputes rather than merely allowing themselves to fight over it. In addition to all of this, the Empire--effectively--provided a government structure above that of the individual princedom.

To understand this, let us turn to the Reichstag, or Imperial Diet as it is often translated. The Diet was the gathering of the estates of the Empire, and to hold a seat in the Diet, was to be a true Imperial Estate. The Estates are best seen as a convention of the Emperor's direct subjects, who could then discuss and present recommendations to the Emperor. The Emperor could then approve of their recommendations to transform it into Imperial law. The Diet could vote the Emperor money or soldiers to meet a threat, among other issues. The Diet consisted of different 'Colleges': the Electoral College, which of course consisted of the Prince Electors; the College of Imperial Princes, which consisted of the non-electoral princes, both secular and ecclesiastical; and the College of Cities, which consisted of the Imperial Free Cities. The Free Cities were a later addition to the Diet, and were inferior to the Electoral and Princely colleges for a long time.

As such, as we can see, the Imperial Princes had a voice in the government of the Empire as a whole. This resulted in what was essentially a diarchy between the Princes of the Empire and the Emperor, with both relying on each other in their own way or manner. The Emperor needed the princes to give their approval for his wars and policies, while the princes relied on the Emperor to provide a centrepoint and the enforcement of the laws and policy of the Empire. As such, the Empire did provide advantages to the average Imperial prince, both in terms of garunteeing their own physical security, and of increasing their own imporance by giving them a voice in the government of the wider Empire as a whole.

Hopefully, this answers your question. Please feel free to ask any follow ups!