why Sauron's plan failed so miserably?

Well first of all Sauron's plan was perfect but he overlooked one small detail, that the rings are connected to each other. He simply underestimated the link which they shared and Sauron himself a creator and master of the ring needed time to learn how to use his ring which was quite new invention never before seen. Elves as it was written ,,perceived that he would be the master of them" and realized his true intentions before he could dominate them properly (as he had to first get to know how it's abilities work and we know it gave power to dominate minds of others not only those who wore rings), note that elves didn't use their rings until Last Alliance defeated Sauron so the One would work on them enslaving powerful elf lords who had the ring in their posession and thus maybe entire race. Small details are often of significant meaning. It was a masterful plot but even the most crafty spider will leave a weak thread to paraphrase Gandalf's words. Yes Ring indeed enhanced Sauron's power Tolkien wrote that his power on earth was greatly enhanced and even without it he was in rapport with it's power. Adding to that he was already a divine being master sorcerer, necromancer, ,,great craftsman of the household of Aule and mighty in lore of that people" he was indeed more powerful than ever. Elves were most powerful of ,,mortal" species (or I should say physical incarnate races cause elves are immortal in a sense so it is understandable that Sauron sought to use their skill, knowledge and powers for himself. Morgoth already done similar thing enslaving many elves (also magically looking into their eyes) and had profit from their skill (mostly of the noldor craftsmen

 

His plan was good in that he created the rings to prey on weaknesses in all the races, Mens weak will, Dwarves Greed and elven belief in their own immortality. Trouble is, he forgot the Hobbits and his own weaknesses too.