Yeah, I don't think this was ever practical. IIRC this was something that come forth from Sweden in association with some of the German princes that advocated strongly for constitutional reform, most aggressively Hesse-Kassel. But Amalia's position was largely passed over by the majority of the Estates at Westphalia. For one its important to remember that while the Empire was a shared sovereignty of Kaiser and Reich it was also still extremely hierarchical. So the position of the German Princes lining up behind Hesse-Kassel threatened not only the Emperor but the Electors as well. Basically the package of constitutional reforms they wanted would have amounted to sharing out the power and prerogatives of the Prince Electors among the rest of the German Princes (the Counts). Certainly putting limits on who the Electors could elect even if they still retained the exclusive right of Election would be kind of a slippery slope. And what defines a dynasty anyways. Could the main branch of the Habsburgs be followed by a Tyrolean Habsburg? A Spanish Habsburg? Could a Bavarian Wittlesbach be followed by a Neuburg?
Anyways there's also the problem finding a viable non-Habsburg candidate. The Emperor is going to be a Catholic, you'd need a much bigger and probably earlier POD to get a protestant elected in the 17th century. But aside from Bavaria the next most powerful German Catholic house of Pfalz-Neuburg followed by Pfalz-Sulzbach (once they converted) maybe tied with Baden-Baden. Slim pickings. And even Bavaria had questionable ability to rule effectively. Besides the Electors are going to be loath to elevate a lesser Prince to a position above them in the Imperial Hierarchy (see above issues) while they all have too much rivalry with each other to agree on one of their own (Brandenburg had conflicts with Neuburg in Westphalia, Bavaria and the Palatine branches had unsettled issues over Bavaria's elevation to the Palatinate's old electorate). Meanwhile Sweden and France would quickly prove themselves too interested in aggrandizement at the expense of the Empire. Sweden almost immediately in trying to annex the Imperial City of Bremen and France later on under Louis XIV with his reunions. So a foreign candidate isn't really viable.
Having said all that I guess if it somehow happened I think it would quickly lead to the weakening of Imperial institutions. The Riechshofrat wouldn't likely function well under a non-Habsburg leaving the Reichskammergericht as the sole functioning court, but it was notoriously underfunded and it had less ability to enforce it's edicts than the Riechshofrat. The Empire also loses an impartial arbiter in many of the petty disputes between minor states if the new Emperor has less authority, prestige or respect. In some ways the HRE could parallel Poland and the issues that the Kings of Poland had in contending with the power of the Szlachta.