Some answers to your questions:
I'm working at a very small local TV channel. We're using a very old software (from 2002) called InfoCaster for playout, but now testing a new computer with OBS. (If you're not familiar with InfoCaster, don't try to search for it! We tried to find them, because we thought it's a good idea to get an up to date version of their software that meets today's expectations of broadcasting, but now there is not even any sign of somewhen that company made playout software.) Nowadays most of industrial standard playout softwares are costs thousands of dollars (per year) what is way more than what fits into the budget of a little eastern-european television, and ironically OBS (with Advanced Scene Switcher) is better in automation, than the commercial softwares (however OBS not a software without compromises too — more about that later).
I think the only advantage of 24/7 (or not continous, but scheduled, regular, frequent) broadcast over constantly available, searchable content is the capability of break through information bubbles. I mean you can find everything on the internet, but you will find only what you search for. So maybe there are many things that would interests you, but you don't even know that those are exists, so you never search for it. But if you follow a channel, that channel can provide such informations for you, so I think the target audience of a streaming/broadcasting channel should be the people who are open for completely new things and the content of these channels should be present various, little-known things in an easily understandable, no prior knowledge required way. This type of content obviously doesn't really work with a one person staff, as it only can reveal topics that is in that one person's information bubble, this require a team. As a local television, we try to find small, exciting local communities, peoples, upcoming events and present them in our programs. It takes three full time job and a few people who help us occasionally to produce all the material for our broadcast, also we get a small part of our programs in broadcast ready state from other creator teams. All these together covering all the tasks at our channel from discover topics to shooting, edit videos, to put everything into the playout software, maintance of equipment, manage YouTube channel. Higlighting from this the need for time to feed the daily programs into the playout software is take about 20-30 minutes. Now it seems OBS can reduce it to max. 15 minutes when we will start using it in live.
We're upload a part of our programs to YouTube after them were broadcasted, but some of our programs quickly losing actuality so those can get most of the views in them scheduled playing time. Some other programs are not own produced and we don't have rights to share them constantly, we get them just for broadcast.
Currently we don't have live programs, but there were many years ago. We have the technical capabilities for it and we want to keep it in order to a live program would only depend on decision, not on technical capabilities. Also a live like recording (when everything is done as would be a live broadcast except broadcasting it) require live capable equipment and it could speed up the workflow of the production.
We don't have real 24/7 playout, we have only 3 to 4 hours of programs a day, in the rest of the time we broadcasting photonews (I'm not sure if it's the right english word for it, basically it's a slideshow with advertisements and information of public interest on the pictures). Because of this program structure we don't have to worry of the small delays caused by processing times when changing files on playout, however I think it's much smaller problem than you presented. The three second is unrealistically long time. I've tried OBS on a lot different computer with very different computing power, but I never experienced more than one second delay on a media change. It is possible that very weak machines needs more time, but very weak machines are incapable for any kind of broadcast managemant at all. Moreover take into account that OBS doesn't know in advance when it will have to change between souces as it try to react immediatly to the users interaction, or the scene switcher pay attention if a condition is true and if it is, than change immediately (not looking in advance, when it will be true), so OBS doesn't have time to get ready for the change, while a time scheduled/playlist software has the opportunity to do that, as it knows the changes in advance, because new medias have exact starting time given by the user, or calculated from the current time and the remaining time of the currently playing media. And if it knows in advance when it will have to change between medias and which file will come than it can prepare for it before the change (e.g. decode and load the firs few frame into RAM). (OBS also has the opportunity to it with programmed changes, but as I know it doesn't take it.)
Our only major problem with OBS as a 24/7 playout software that it cannot provide a list of what and when will played with the current setup. It provide much more effective automation tools than industrial standard softwares for a rigid program structure as ours (when same type of programs come in the same order on every single day or week, however it much less usable for constantly changing structures), that's why it can speed up the work so much for us, but the missing of a list of what it will do let make mistakes easier. And it is enough to set up only one thing incorrectly and it won't start a media when we want to start it or start other than we want and it'll result that nothing after that in the chain will start. A little mistake could make a complete disaster, because we can't check on a simple list: is everything correct that we setup?