When I saw this ELL question it struck me that very delicious didn't sound vary "natural" to me.
Checking Google NGrams, I find that relatively speaking, toothsome food is five times more likely to be described as delicious rather than tasty...
...but if the intensifier very is present, that preference reverses. Things are actually three times more likely to be very tasty rather than very delicious.
As a native speaker, I already knew intuitively that the preference existed - and it was no surprise to me to discover how strong it was, since otherwise I wouldn't have been aware of it in the first place.
But I can't think of any reason for the difference. It's not obvious to me delicious has any greater sense of being a "non-gradable" attribute than tasty, so I can't see how the phenomenon can be rationalized by analogy with, say, very unique, very dead, very perfect.
Please don't just closevote this as "matter of opinion", or brush it aside as "established idiomatic preference". I feel there must be some "reason" causing such a marked preference, since it's so consistently observed, but it can't simply be that we repeat what we hear others say, since neither of the "intensified" versions occur often enough for an average speaker to consciously notice anything. I feel that somehow or other we must all be influenced by the same underlying principle, without being consciously aware of it.