It's not particularly hard to keep up with those number of shows. I also read about a book or two a week and play video games besides working a 9-5 job. Then again, I'm a bit odd.
I generally subdivide and think of my time in blocks and units. I'm also efficient with my time. Outside of the first time I skip OPs and EDs and next episode previews. That leaves an anime episode around 22 minutes give or take, which means I can hit about 3 in an hour or so. I generally cook and eat while watching so that it overlaps with the time I would normally eat dinner, however long that takes so I'm not wasting time where I could be multi-tasking, eating doesn't require much concentration. So if we take it like that, I only need let's say...5 1 hour blocks a week to watch 15 shows. That's easy enough, I could do that on my workdays during dinner.
That is, of course, assuming that I keep up with every show I watch weekly which rarely happens anymore unless it's something I'm really eager about. Most of the time I just wait til a show's cour is done and watch it all at once. We're talking normally 12 or 13 episodes at ~22 minutes each for around 4 and a half hours per show. That's something I can watch after work. If we're on the weekend, let's give myself 18 hours or so (I don't sleep a ton). With that kind of time I can watch 2 shows a day and still have time to do chores, run errands or hang out with friends. Some of those can even overlap; watch it while doing laundry and folding or somesuch.
It's not really that difficult. If you want to do something it's always possible to find a way to make the time for it if it's important enough for you.
I'm an oddball though. I'm a writer and any interest or hobby I have I have what can only be described as a ravenous appetite towards it. I don't go halfway or casually into my interests. If I'm gonna watch anime, I'll watch all the anime I can. If I can read a book I'll buy everything by the author and stay up til 4 AM when I have to get up at 730 for work. I want to absorb everything I can from a medium I'm invested in. It gives me a much higher tolerance for shit than most anime watchers. If something had an interesting take on a power but was otherwise as generic as can be, I'll probably finish it because the interest in that can carry me through a show. If one of the characters is written even somewhat differently than a normal shonen lead, sure I'll see it through. If I can find one or two redeemable qualities in a show then that's normally enough for me to consider it worth at least that one watch. It's not always the case, I'm weird in that some things can set me off in an otherwise great show that make it unwatchable for me. I find it extremely hard to get through Shaft shows, especially those that flash text quickly across the screen. This irritates me an enormous amount because I dislike missing anything, even if it's not important or not supposed to be seen really. It just ticks off a box that makes me unwilling to look past it. Then again I've also watched the worst shows in existence just because I liked the character designs (and anyone on this forum can attest to the fact that my taste in design is pretty atrocious weeaboo trash).
I also have a tendency to write really long explanations about my passions that no one thinks that heavily about or gives a fuck about.
tl;dr Kamisama Dolls was pretty good.