But as to the genesis of your post, there's a simple problem that can't be denied. Even the lightest AT set-up (I'll use mine only as an example) is going to be shy of 17 pounds or so. Heck, call it 15. Snowshoes? Mine are Tubbs Mountaineers. Beefy 25" tanks that I love. They have an aggressive claw and heel risers; there's no way anyone would call them featherweight. How much do they weigh? 2 lbs. 5 oz. for each, 4lbs. 10 oz for the pair. Given the excess weight on your feet with AT gear, that probably explains the difference in uphill performance vs. much lighter snowshoes. Hard to stay even going uphill with such a disadvantage.
rando racers' gear is a whole lot lighter than that- a bit over 3lbs (pair) for the skis, a bit under 4lbs (pair) for the boots, just over 1lb (pair) for the bindings, and skins aren't much on the tiny short skis those guys use.
As for more normal AT gear, yes, it is true that it weighs more than snowshoes and hiking boots. However, a key element of skinning is that you rarely lift that weight- it's all about the stride and the glide. Anyone with good skin technique will leave their skis on the ground the whole time except for switchbacks. And the stride on flat ground is much longer than that of a snowshoer. To make an analogy, would you rather pull 4 cinder blocks on a sled over snow, or lift 2 cinder blocks up and down over the same ground? I'd rather pull the sled. Given all the inefficiencies of snowshoes, I have a hard time imagining a snowshoer even remotely keeping up with an experienced skinner. Skis have been around for at least 10,000 years as a mode of winter transportation for good reason. Snowshoers certainly couldn't keep up with skiers at 24 hours of sunlight, even disregarding the downhills.
As for the original question, the weight of alpine boots is an issue, but there are a number of other areas where AT boots are vastly superior. The vibram sole is a huge help on rocky terrain (and for riding snowmobiles for access.) The walk mode is a huge deal for getting a good stride, like I talked about above. Even more important with the walk mode is the ankle dexterity that you can't get with alpine boots- which is important for technical ascents and cramponing snow- the forward lean inherent in alpine boots is tough to deal with on an extended snow climb.
That said, keep in mind that Sean Crossen skied all the 14ers except Capitol with not just alpine boots but also alpine trekkers and atomic alpine bindings, which are really heavy. I stuck with a similar set-up for a long time waiting for an AT boot that I liked before all the newer, stiffer AT boots came out in the last few years. It's tough, but they sure do ski nice on the way down