Although I've never played a game without running shoes (except Pokémon Ranger, where they walk faster anyway) I would hate it if they weren't there. Although I mainly just walk at normal pace while I'm progressing through the game, they make dashing about between rematches and berry plots so much easier, especially if you're stuck with the Acro Bike or just don't want to listen to the bike music (Although bike music isn't bad, it gets irritating when you have to sacrifice route music in order to travel fast).
And not Gen III, but I loved how Hg/Ss gave you the perma-run button. Taking it away was the only way Black / White could be seen as a step back from previous gens, rather than building on them (I won't say improving because you can argue some things weren't any better e.g. Sturdy)