What study backs up such a statement? Please give a link to it/them. I've never come across a study that proves or disproves this and I've looked hard for one. My single-topic-channel advice comes from decades as a marketer.
Countless businesses have tried a diversified approach or focus approach. Those who do a diversified approach only succeed as long as they have little or no competition. Once a focus-approach business comes in, the diversified-approach businesses have an increasingly hard time holding on and most eventually fail. Death by a thousand cuts. Each cut done by a different specialty business. The Five & Dime stores are a thing of past. Everything-including-literally-the-kitchen-sink Sears is dying a slow painful death. Specialty stores and the Internet (the home of the ultimate specialty stores) are the reason. In comparison to Sears, Wal-Mart is far more focused. Look at TV. Variety shows used to rule it. With literally hundreds of niche cable channels today, the closest we get to that today is something like American Idol.
And when a focus-approach business tries to diversify, they rarely succeed. McDonald's has for decades tried to crack into the supper market (anyone remember the McSteak?) and has yet to succeed. Even at a corporate level, whenever McDonald's has tried to diversify their corporate portfolio, their core business (McDonald's) has suffered. Only after a new CEO comes in, sells off all the non-McDonald's businesses, and refocuses the corporation has it rebounded. This cycle has repeated itself over and over again at McDonald's.
As for YouTube, the above might also be in play. When YouTube was young, variety channels could succeed. Like early TV (the "golden" years), no one had much of a clue what would work on YouTube ... if anything. But now there are so many channels being created everyday, variety channels have a harder time standing out or even being heard. Niche channels is what every successful YouTuber that I've read about has been saying is the future of YouTube. Niche channels succeed partly because they are easily searched on search engines and develop a dedicated following for their single topic. Sure, there are some old successful channels that were variety channels when they started, succeeded, and remain so today, but you cannot say what worked in YouTube's infancy (and the successful channels that came out of it) would work today and I've never read any successful YouTuber from that era advocate a variety approach today. On the contrary, I have heard of tons of YouTubers who started a single-topic channel and then later tried to diversify and then complain to High Heaven on how many subscribers they lose because of doing so. The best advice I've heard from successful YouTubers is if you want to dive into a new topic, start a new channel about it. Don't blend. Separate. Promote all your channels at the end of each video, but don't mix. This advice going as far as making a channel for your vlog videos. Make the vlog videos into a support channel for your main channel.
But if you can give links to studies that back your statement, that would be great. I would love to read them.