There are zero situations where if your hardware is not good enough to run a game that upgrading from a HDD to a SSD will allow you to play that game.
I never claimed this specifically, but it isn't wrong either. Whether you call some level of performance "playable" is subjective. If I deem the FPS boost I get from installing DayZ on a ramdisk worthwhile (however small it may be), where it wasn't prior to having done this, then yes, I did just make a game playable by having upgraded the storage that the game was installed on.
What I was arguing is that installing a game on a faster hard drive sometimes makes the game run better - depending on the implementation and resource demands of that particular game.
What you're actually talking about, even though you don't realize it, is loading times.
Yes, load times perhaps running concurrently to game-play. We have the technology to spin up new threads and processes - this is 2016. This loading could, by the way, use up system resources, and hence affect performance.
A SSD will help in this regard because assets can be loaded into RAM faster, so they're more readily available in the game.
This point doesn't even matter. Of course data has to be read into RAM before it can be accessed by the CPU - I never said that it didn't. However, if you look at this proposed model, you will see that you are still fucking reading from the disk, whether it goes through RAM first or not. Perhaps I should also mention that, before the CPU can technically do any operations on the data stored in RAM, it first has to be written to one of the CPU's registers. Maybe I should mention that, before any math can happen, the data has to be written from that register to the accumulator. Maybe I should mention that before you can even fucking load anything anywhere, you have to push your subroutine callback onto the stack. I won't, however, because it doesn't matter; you are still, even if only in specific cases and to often negligible effects, waiting on the disk.
Also, not all of your shit can be in RAM at once, hence why you have to clear RAM and read what you need at that moment from the disk.
The reason this can be helpful in competitive games is when an enemy shows up within your draw distance, before he can actually appear on your screen the assets for his character have to load.
This is akin to textures loading up as you traverse the WoW over-world. This is also akin to textures loading up in ArmA as you fly over the several square kilometer playable area. You, however, seem to disagree with me on these two specific examples.
That said, 9 times out of 10 to increase performance upgrading your RAM is more beneficial than upgrading your HDD.
Now, you're actually right here, and for a funny reason. Adding RAM to a computer that isn't using all of the RAM it already has, doesn't really do much. But, the operating system will use that space as a disk cache, which would speed up read access from the disk. AKA: You're only right here, because having a faster disk (in this case a pseudo RAM-disk, as previously mentioned) will speed up certain operations.