I was going to post about how LttP did have Link increase speed, but I realize now you're talking about those Graal ice scripts that make the player start flying across the screen(or at least I think that's what you're talking about). I haven't seen one of those in a long time, though.
0:48 in and you'll see how link gains speed gradually(but still fairly fast) when he starts his walk. Ice on LttP was actually dreadful, and one of the experiences I hated. Especially trying to work your way into doorways and the stairs.