If pages are not needed, they will be reclaimed and used by the kernel to do whatever it wants, whether or not they are backed by swap.
Kernel is now deleting data randomly? A new thing to me!

No, they will not be reclaimed. Anonymous pages continue to exist until all processes release them. Kernel can do nothing about this.
Anonymous pages that have been written to and need to be kept alive are eligible to be swapped, but the kernel can't predict their future, and if they are swapped out, latency on the next access will go through the roof. So in general, the kernel avoids doing this unless it is in memory pressure. Presumably the application allocated that memory anonymously for a reason, instead of mmaping a file.
Yes, kernel does not evict pages from RAM unless it needs RAM. Any pages, not only anonymous. This is obvious, almost a tautology. What was the goal of mentioning this?
This is less correct than the naive idea you are trying to refute, which is overly simplistic but basically correct.
Whatever you think of the picture I presented, the refuted idea is not “naïve” or “simplistic”. It is outdated and incorrect in terms of how memory management works today and for what kind of operation it is being optimized.
You even mentioned anonymous pages yourself. Backed pages are an important use of RAM for code and file I/O, but the vast majority of memory utilization on most systems is not file-backed, it's just whatever working memory your browser and whatnot needs, which will never be written to disk (unless it gets swapped there). So one of RAM's roles is to act as a buffer & cache between the OS and non-volatile storage, but that is not its only role by any stretch.
One can’t make an argument against a statement by negating the statement and using that negation as the argument. And this is what you did here, I believe. “Your picture is wrong, because: let’s assume the picture is wrong, therefore it is wrong”. Perhaps there is some miscommunication in either direction?
For example on the machine I am typing this right now, there is more than 3x anonymous memory active than file-backed memory:
Then in my opinion your system is having not enough RAM.
(1) If we are in the “for example” territory: on my machines:
Active(anon): 1122960 kB
Inactive(anon): 536088 kB
Active(file): 3026396 kB
Inactive(file): 412788 kB
Active(anon): 20384 kB
Inactive(anon): 2604 kB
Active(file): 89520 kB
Inactive(file): 431008 kB
This is more or less true, as it was in the 1990s as well, and sometimes it is the only solution
But in 1990s it was both the accepted remedy to use swap and the goal of having swap in the first place. Nowadays it is neither the solution, nor a goal of having swap. The general movement recently is to even abandon swap altogether as inherently harmful. With a countermovement of people subscribing to the
view explained by Chris Down, to which I myself belong.
but on the kind of machines we're talking about, desktop workloads with 32-64GiB of RAM, it's rarely needed. But whether or not you need the swap, the kernel will opportunistically use it to prepare pages to be evicted quickly. Having it enabled will definitely increase writes to your storage, whether the kernel ever actually commits pages there or not.
The same hypothetical argument can be made in the opposite direction: that the kernel may in some circumstances force dirty file-backed pages earlier than needed, increasing writes.
In both cases for a 64GiB systems I do not see this being a significant issue.
(1) With an exception of a particular situation, when one works mostly with webapps. Which by their very nature are ephemeral and must be stored in anonymous pages.