In short it's a trade off between your resources and the supposed resources of the attacker. Even though SO14 escorts "heads of state" they don't escort the US first lady, etc. they bring their own apparatus.
So, since SO14/Britain couldn't do what the US does, because it would be too disruptive and cost too much given the level of threat and resources, the US secret service can. They have both a higher threat to deal with, and the resource to do so.
It's the same as in the military. If you just want to know what's going on, sneaking a four man recon patrol in, using maximum stealth is the way to go. However, if you expect the enemy to be too thick on the ground for that (problem with small patrols is that they go missing all the time, and then what?), an armoured reconnaissance battalion is the way to go. So either go very small, or sufficiently large. If you can't cordon off the area and man the whole route, then go small and stealthy, trying not to give away anything. If you can, then you go whole hog, complete with barriers and "x" number of officers per yard of road travelled.
This of course also depends on your objective. If you check the SO14 film, it's a couple of cars. The presidential motorcade OTOH isn't that far off in size from an armoured reconnaissance battalion (well, company at least), so they have to behave like one. You couldn't bring that kind of mass of vehicles and people through on a contingency basis anyway, all traffic would grind to a halt, and the smallest fender bender ahead of you would make you a static target. So, you're basically forced to go the whole nine yards anyway, and hence you have to do it properly.