Unity's parkour is #1 simply for being faster than running
In AC 1 to 4, running is genuinely just a better thing and faster to do than climbing or using parkour. Parkour is slower than just running to your destination, especially in AC 2 and 3. Connor was just Usain Bolt, so running was always the best option unless it was a snowy environment.
Same with the Ezio games. It's just overall better to run to your destination. Or use a horse, in the case of brotherhood.
In unity, Running to your destination takes ages amd is generally slower than using parkour to get there. It's better because it actually had practical use rather than just feeling good to do. Syndicate continued tye bullshit with carriages being faster than parkour, mirage and shadows also continued this trend. Running or riding a horse is generally better than parkour.