First of all. You aren't going to get many replies to your question. Because the SNES didn't have many RPGs without random Encounters. The system both wasn't strong enough to support large amounts of sprites on screen and the carts space didn't allow for large amounts of data. Only last gen games which were 32 Bit were able to push that envelope. Games like Chrono Trigger, Seiken Densetsu 3 and Terranigma. Secret of Mana was a good experiment, but as you surely found out by playing it, it had tons of glitches, lagged often when more than a few enemies were on screen and response time for your own character was slow. Because it was an earlier SNES game.
So, the 'non' Random Encounter games had to wait for a more powerful system.
This means most of the RPGs on the SNES have Random Encounters. But that doesn't make them bad. In fact, the same guys who made Chrono Trigger made probably the best RPGs on the system after Chrono Trigger. Dragon Quest V and Final Fantasy VI.
Six upcoming games you should look into:
