On the other hand, it is possible to run out of a metal when all of it is either somewhere in some device or scattered among landfills (i.e. not concentrated in a place like a mine).
That is true, but gallium is present in the aluminum and zinc ores only in minute quantities.
We will not remain without gallium, but it is impossible to scale up the gallium production to a higher level than provided by the current productions of aluminum and zinc.
So there is a maximum level of gallium that can be used per year and it would not be possible to increase the production of blue and white LEDs and of power transistors above that level.
Fortunately, the amount of gallium used per device is very small, so it is not likely that we will hit that level soon. A much more serious problem is the associated consumption of indium, for which the resources are much less.
Practically speaking, sure. It's obviously not cost-effective to extract it. But it's there if someone can get it. I don't expect anyone to be extracting gold from ocean water, but there are other source of other elements that may not be cost-effective now but could be in the future or may simply become necessary despite the cost.
Cost scales with refinement effort, so it just results in more expensive TVs. That said, pretty sure we'll have drowned the planet in landfilled TVs long before this becomes a serious issue