I've done it both ways. I typically grill 1.5 inch ribeyes. First of all, if you really think there's only 1 tsp of juice coming out of a thick ribeye like that will all that fat, you're just wrong. When I pulled the ribeyes directly off the heat and sliced, the meat itself was just very tight and there was juice and blood that ran everywhere. When I rested on a plate loosely foiled for 10-15 minutes, the meat had relaxed and there wasn't nearly the amount of juice and blood left on the plate. Also, letting steaks rest for 10 minutes doesn't make them cold. They're still between warm and hot after that rest.
I'm just telling you I've tested this theory and it didn't work out the way you describe. Maybe you're talking about a sirloin or another different cut that's much more lean than ribeyes. But there was a massive difference when resting the ribeye.