As stated before, without the disaster of Sicily the mines of Laurion would be far less vulnerable and Athens would have far more manpower to put toward controlling its slave population there. Pericles strategy didn't fail, before the plague it was successfull and by all accounts Athens was able to keep paying for its war effort without too many problems until it started to have its allies revolting, which they didn't dare to do except in isolated cases until the Sicily disaster. The plague was bad luck, nothing more. After the Athenian population continued to be boxed in the city and no other large scale epidemic happened and Nicias being in charge had as much to do with Cleon death then the military situation. In any case, the voters would turn back toward a more agressive stance pretty soon afterward...
To say that Sparta kept challenging Athens at sea is also really pushing things: until Sicily it only did so once, and its fleet was soundly defeated by Phormion, putting the matter to rest. That Athens didn't invade the Peloponesus all the time also didn't mean they where inactive on land: campaigns where pursued in the north east and a large scale invasion of Boetia was launched. Not counting Mantinea is also problematic: even while Athens didn't contribute a massive force, which she should have done and didn't do because of Nicias obstruction, the coalition was still built and kept together by Alcibiades politicking, it also would never have happened without the blow Sparta took at Sphacteria. Similarly, saying that only chance made Pylos possible is also oversimplifying matters. Desmosthenes had the strategic conceptions behind it beforehand and was ascendant in Athens political horizons, he would have had excellent chance to carry his idea out at some point even without the storm. While they didn't destroy it the raids and Pylos did very much took their tools on Spartan agriculture too.
All and all, by the very nature of its system Sparta was always very vulnerable, a significant defeat like Sphacteria was enough to cause a massive crisis and a big one, like Mantinea could have been and Leuctra eventually was, was bound to end Spartan power altoguether. In contrast, Athens was able to endure a series of cataclysm before its final defeat.
Moresso, the two cities still had two much conflicting interests for peace to reign and the reasons who pushed Sparta to war in the first place where still very much there. They would have gone for another round and without the Sicilian disaster, let alone with Syracuse taken, Athens would have entered the new phase of the war with the deck very much titled in her favour.
Sure, Sparta was vulnerable. But even with Sphacteria, the Spartans were able to keep the war going for four more years and gain leverage to make a more equitable peace. It was more of a psychological blow, not a physical one, since it didn't lose Sparta the war.
Periclean strategy failed. It was designed to make Sparta seek peace within a short period of time by relying completely on the defensive except for minor raids that did no damage compare to the damage that was happening to Attica. It was designed to make Sparta seek peace within three years or so. Pericles had no plans on making a fort on the Peloponnese, or to capture Spartiates in an island. It did not involve invading Boetia. Notice that while Pericles was alive, he did none of those things.
Pericles wanted to force Sparta to peace within three years by a largely defensive strategy on land.
It failed in that. Sparta did not seek peace within three years. Therefore, it failed in its purpose. The Athenians abandoned his strategy.
Even without the plague, the Periclean strategy has failed.
And yes, it was a fluke. Demonsthenes had a plan, yet the Athenians did not approve it. Only when there was a storm that forced him to Pylos, and only when another storm caused him to delay departure and to make a fort, was that plan accepted.
Without the storm, Demosthenes would not go to Pylos but continue on to Corcyra. It was pure chance.
Yes, Sparta kept challenging Athens at sea. How many fleets did Sparta lose until they eventually won the war at sea? Many, many more. Yet they kept going at it until they won.
Contrast it to Athenian relative inactivity in the Peloponnese.
Even with the nature of the Spartan system, it was not challenged by Athens in a way that would win it the war. Even the fort at Pylos was not the war winning blow that sent Sparta to its knees.
Athens also was vulnerable. It must have a powerful fleet, or it would lose. Lose that, and Athens would surrender. Sparta could lose fleet after fleet and not be defeated, as OTL showed.
As it did in 404 B.C.
Mantinea was the best chance to defeat Sparta on land, I agree. But it the only time that Athens could do so. Any other time, Athens could not damage Spartan power.
While Sparta was eventually able to wear down Athens.
I disagree that the two cities could not live in peace. The idea of Thucydides that the Great Peloponessian War was inevitable was contradicted by his narrative. It only arose because of Corinth going to war with Corcyra, and Athens accepting the Corcyran alliance, but that was only because of the civil war in Epidamnus. Without it, the Peloponessian War would not happen at all. The reason Sparta went to war was because Athens interfered in the Peloponnese by imposing the Megarian Decree, and making an Alliance with Corcyra while that city was at war with Corinth, which was a member of the Peloponessian League.
And even then, without the prodding of Corinth, Sparta would not even have gone to war. And even with such prodding, Sparta would not have gone to war had Pericles rescinded the Megarian Decree.
Simply put, it was oversimplifying to say that it was fear of Athens that drove Sparta to war. It was not. It was a specific set of events that led to war, but such events were not inevitable. Keep in Mind that King Archidamus II was opposed to war, and only the events above caused the war party to gain power over him.
Keep in mind that there are peace parties in both AThens and Sparta, and normally, both parties were in the ascendant. It would take a very specific set of events that would lead to the war party gaining ascendancy. An Athenian victory at Syracuse would strengthen the peace parties of both cities.