Random encounters are fine… in moderation.
They should only happen after a fixed battle has happened—specifically the battle that teaches you the games battle mechanics.
Additionally, most modern games with random encounters have some form of spell\equipment\item\option for encounter rate reduction\negation, and a handful have the same for increasing the encounter rate… no idea why.
But if you go to another town, and the only save spot is in your house, you could be in for a long walk, depending how big the playable area of the game world is. Having to travel far from your location to save, then go back to that place after saving can be a huge issue.