Before I begin, I will point out that I play SWAT almost exclusively, and that the majority of my rank is from SWAT (I'm a Noble, by the by).
Swat originated as a custom gametype in Halo CE, and became popular in Halo 2.
The main goal of Swat is to take away everything that makes normal slayer what it is, until you are left with the basics. You, a precision weapon, and the potential for a crap-ton of skulls with holes in them.
There have been a few variations of Swat that were really fun, but those changed weapons while leaving everything else normal (i.e. no equipment and only sprint). Some of the customized Swats include (but aren't limited to) SWATguns (where everyone has shotguns and no shields or AA's), SWipers (everyone has snipers, and again no shields or AA's), and SWAssault (everyone has an AR and a pistol, but no shields or AA's). Mind you, when I say no AA's I mean sprint is still included, but other Armor Abilities are not.
SWAT with armor abilities would become an armor locking fest the likes of which you've never seen. The reason being that you can still aim while in armor lock, while your opponent cannot harm you and only has a limited idea of where your head will be. Seriously, anyone who didn't use armor lock would be labelled an idiot.
And you think people who use bumper jumper are bad? Just wait until you put jetpacks into SWAT. People will be spamming it just to make them harder to hit, rather than using it to fly around.
Evade in SWAT would also get annoying quickly, because it is very hard to get a headshot on a rolly polly. Not to mention that it would be pretty OP, because all you'd have to do is shoot someone once then evade into them for the pummel kill.
Active Camo would be VERY OP in SWAT, and would turn the game into a camping trip from hell. Since there is no motion tracker, people could just sit in corners and camp, and no one would know they are there until they get killed.
Hologram wouldn't be too bad, but at the same time Hologram seems to have the ability (when it's first cast) to block incoming pummels and headshots (and yes Twinreaper, I did test this after our last go round, and it does), so that would make it annoying as well.
All in all, armor abilities in a gametype without shields would make it suck. Hardcore. And the reason that SWAT doesn't have motion tracker is because that would make camping easier than it already is, which would ruin the gametype too.