I think random encounters are more of a mental barrier than a gameplay one. I mean, there are games where you indeed can see the enemies AND avoid them, but in those games you often still have "traps" and similar where you can't avoid the enemies jumping towards you as you approach a chest. I don't mind random encounters much, a high encounter rate is much more bothersome. I mean, if I feel that the encounter rate is low when running around, I'm much more at ease and more willing to explore than when I run into battles every other step (see Tales of Destiny).
And well...you can avoid enemies in games with random encounters too (escape)....so I think the speed of the battle system is an important factor as well.
And Wyzdom, have you ever played Wild Arms 2 and 3? Both games use a system where symbols appear above the head of your character before a battle will ensue. If the symbol is green though, the battle will be against enemies of lower levels. And by the press of a button, you can simply avoid it.