You describe epigenetic inheritance. It is real.
https://en.wikipedia.org/wiki/Transgenerational_epigenetic_inheritance
Transgenerational epigenetic inheritance is the transmission of
information from one generation of an organism to the next (i.e.,
parent–child transmission) that affects the traits of offspring
without alteration of the primary structure of DNA (i.e., the sequence
of nucleotides)—in other words, epigenetically... For some
epigenetically influenced traits, the epigenetic marks can be induced
by the environment and some marks are heritable, leading some to view
epigenetics as a relaxation of the rejection of the inheritance of
acquired characteristics (Lamarckism).
It makes sense that this could be adaptive. Genomic adaptations involve a lot of luck. If you can pass down to your offspring something you have learned the hard way, it will save them a lot of grief. An example: mice who learned to associate an odor with trouble passed that on to descendants via epigenetic genome modulation.
https://www.nature.com/news/epigenetics-the-sins-of-the-father-1.14816
Dias had been exposing male mice to acetophenone — a chemical with a
sweet, almond-like smell — and then giving them a mild foot shock.
After being exposed to this treatment five times a day for three days,
the mice became reliably fearful, freezing in the presence of
acetophenone even when they received no shock.
Ten days later, Dias allowed the mice to mate with unexposed females.
When their young grew up, many of the animals were more sensitive to
acetophenone than to other odours, and more likely to be startled by
an unexpected noise during exposure to the smell. Their offspring —
the 'grandchildren' of the mice trained to fear the smell — were also
jumpier in the presence of acetophenone. What's more, all three
generations had larger-than-normal 'M71 glomeruli', structures where
acetophenone-sensitive neurons in the nose connect with neurons in the
olfactory bulb. In the January issue of Nature Neuroscience1, Dias and
Ressler suggested that this hereditary transmission of environmental
information was the result of epigenetics — chemical changes to the
genome that affect how DNA is packaged and expressed without altering
its sequence.
It would be good to keep a genome. There might be stuff in there you only need (it only needs?) every few hundred years. But how different are Darwin's cumulative "particles of information" from "chemical changes to the
genome that affect how DNA is packaged and expressed without altering its sequence"?