No, it's really not. Joining words into a compound word enables the new compound to take on new meaning and evolve on its own, and if it becomes widely used as a compound it always does so. The term you're looking for if you care to google it is an "open compound noun".
A dog in the sun may be hot, but that doesn't make it a hot dog.
You can use a towel to dry your hair, but that doesn't make the towel a hair dryer.
Putting coffee on a dining room table doesn't turn it into a coffee table.
Spreading Elmer's glue on your teeth doesn't make it tooth paste.
The White House is, in fact, a white house, but my neighbor's white house is not The White House.
I could go on, but I think the above is a sufficient selection to show that language does not, in fact, work that way. You can't decompose a compound noun into its component morphemes and expect to be able to derive the compound's meaning from them.
You wrote so much while failing to read so little:
> in most cases
What do you think will happen if we will start comparing the lengths of the list ["hot dog", ...] and the list ["blue bird", "aeroplane", "sunny March day", ...]?
No, I read that, and it's wrong. Can you point me to a single compound noun that works that way?
A bluebird is a specific species. A blue parrot is not a bluebird.
An aeroplane is a vehicle that flies through the air at high speeds, but if you broke it down into morphemes and tried to reason it out that way you could easily argue that a two-dimensional flat surface that extends infinitely in all directions and intersects the air should count.
Sunny March day isn't a compound noun, it's a noun phrase.
Can you point me to a single compound noun (that is, a two-or-more-part word that is widely used enough to earn a definition in a dictionary, like AGI) that can be subjected to the kind of breaking apart into morphemes that you're doing without yielding obviously nonsensical re-interpretations?
A dog in the sun may be hot, but that doesn't make it a hot dog.
You can use a towel to dry your hair, but that doesn't make the towel a hair dryer.
Putting coffee on a dining room table doesn't turn it into a coffee table.
Spreading Elmer's glue on your teeth doesn't make it tooth paste.
The White House is, in fact, a white house, but my neighbor's white house is not The White House.
I could go on, but I think the above is a sufficient selection to show that language does not, in fact, work that way. You can't decompose a compound noun into its component morphemes and expect to be able to derive the compound's meaning from them.