The reason you (I mean people in general, not just you) are not getting more is because of what you have installed on your phone. In your case, the fact that you say the CPU is loaded should be a clue something isn't right. You should be able to get a full day with anything even remotely modern unless you're a pretty heavy user, in which case an extended battery should work. If you have a phone capable, I don't buy phones without sd or internal batteries, stop buying into trends.
So what's doing it?
Social media is one of the single biggest battery killers, widgets that constantly update (news and weather) are the second largest, with apps in general falling into third. Want to truly kill your battery, use a free ad based widget that handles your social media. It's bad enough you're using social media, which uses lots of data, but as a widget it's constantly updating and often using alarms and such to tell you it has updates, and if it's a widget, it also has to format the data for the widget every time it updates. If it's ad driven, its constantly updating advertisements, and worse still, the ads access the GPS every time too. Some will even turn on the wifi radio for data, location and data gathering (spying), which, while saving you data, uses a FAR less efficient radio. The same applies to weather and news widgets. Keep in mind, they don't share the radios when on, one will wake it, update, power down, then the next can kick them right back on and update. too many things, as is the case here, and the phone rarely gets a chance to idle down long enough to hold a charge.
So what can you do?
Get rid of the social media widgets, period. You can keep the social media, but lose the widgets. If you use a weather widget, use one without ads if possible, and instead of having it use GPS, lock it to either your work location or home, this way it's not pinging the GPS, which uses a lot of power and adjust it, if possible to only update every 30 minutes, or if you turn on the device. You may have to try a few weather widgets to find one that is efficient, some are insanely wasteful. Get rid of anything that puts an ad anywhere except inside itself and runs at boot, yes you may actually have to pay for something. Keep in mind, even some pay apps are tracking you for no good reason, I've called out developers on this in the past. Also, take a look and see what running at startup, in Androids you can see all running apps and in some cases shut them down, but some do it for no reason, uninstall them if they misbehave.
If you are using a "battery tuner" or "trainer", especially a free one, you are doing more harm than good. Yes, they can work, but in my experience they cannot beat what I posted above. Why? Because you are relying on yet another app to do what you should be doing. Why would you use an ad driven battery sucking app, to try to control the other ad driven battery sucking apps. Android has a way took and see what's using the battery ram and cpu cycles which you can use to help diagnose which apps are being battery vampires. Another to be careful of, on at least one phone I had, the "battery saver" or "efficiency mode" actually ate more battery, I'm not sure if this was because of a bad profile or because it idled down below a threshold that was too low for something the background or what, but for some reason it ended up costing me 20% of my battery runtime when I used it.
Lastly, if you are rooted (I can't stand to use one without root), remove factory boat and run an adblocker and/or firewall, you may even want to consider installing a rom, which deletes the factory bloat, adds efficiency, an removes some spying abilities of the manufacturer. There is also some apps which will let you strip or block apps from using GPS or even networking, while they can be helpful, be careful, they can break apps (uninstall the app and simply re-install will fix it).
So does it work?
Well, I can get 1-2 days on a Galaxy S3, about 2 days on a Galaxy S4, and 3 on an S5 (this is with very minimal use), so I would say yes. Under my normal use, in general, I lose about a day or so, but that still bows away the 16 hours at idle requirement. I do run root, and when possible I run either a rom someone else made, or make my own (I now make sure can do this before buying). By doing all this, you may also find you don't need such a powerful CPU or as much ram, since you aren't bogging it down with garbage. I consider myself a power user and can still get by with an S4, though I'm on an S5 now (arguably one of the best phones made).
No, you shouldn't have to be this extreme, but this is reality. Systems are not all that smart, people are too cheap to pay for apps and companies are greedy. Are some of these tactics nice to developers? No, but like the ad industry, they did this to themselves, and before anyone complains about how I'm ripping them off, I'm a developer myself. So, meh. As they say vote with your wallet, lest anyone think it's not working, the fact that the ad industry is in a panic over ad blocking should tell you it most certainly is