How long it takes to take care of an animal can vary from hunter to hunter, afterall it's not a competition, just a task at hand. That being said, We haven't gutted a deer or elk in nearly 10 years. I'd rather leave the mess in the woods if possible. Most game we harvest here in Idaho isn't near roads, most have to be packed out on your back, or the use of stock.
Like many I've done it both ways and it's never affected the taste or tenderness of the meat, gutted or not!! Not gutting is much quicker easier and cleaner than gutting, too it's not a problem at all to secure the tenderloins with this method, you just have to know where to look. I also enjoy the heart as well, I remove that without gutting as well! The removal of neck meat and rib meat is easily done with this process.
I think what happens most the time is hunters aren't prepared to handle game this way, in order to care for it properly you should have game bags with you when you hunt. Once meat is removed, in the bags the meat goes for easy transportation, whether you have to leave it to get help or packframes. Always be prepared, the gutless method is quicker and cleaner than gutting in compared to the old way, regardless of speed! elknut1

With this method I do not bone out the animal. I remove all 4 quarters, then the backstrap, then tenderloins, then heart and misceleaneous. Both hindquarters get their own bags, both fronts the same as well as backstraps and tenderloins and misc. divided into front shoulder bags. All bags are fairly equeal in wt.