Pets are currently set at walking speed. I think it would be a nice cosmetic change if when you enabled run that they could still be hot on your heels It would be a very small change, only a few lines of code depending how the pet classes are setup and it would almost negate the need for the summon pet button which only serves as UI clutter.
Some pets can actually run, and they toggle their speed together with you. It's probably the older ones that can't run (yet). Support on making the older ones run as well.The RS Wiki needs a hand, and Bwian's will gladly take the rest of your body!
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This has made a lot of people very angry and been widely regarded as a bad move.