For me, it helps to think of verbal ("-i") adjectives as the same thing as a verb. Or rather, that they're both just predicates about the topic.
tanoshikatta is literally a predicate stating "was-fun", and desu is just a formality afterwards to make it polite.
this differs from the other kind of adjective ("noun adjectives"), which can't conjugate themselves, so you need desu to change instead.
Of course, the even more polite form is "tanoshuu gozaimashita" (which comes from tanoshiku gozaimashita), but even then it seems to me to be the same form as tanoshikatta if you accept that the latter could've derived from "tanoshiku atta".
I'm not a linguist though, so I do not know if the above ideas are correct, but it's the way I understand Japanese verbs.
tanoshikatta is literally a predicate stating "was-fun", and desu is just a formality afterwards to make it polite.
this differs from the other kind of adjective ("noun adjectives"), which can't conjugate themselves, so you need desu to change instead.
Of course, the even more polite form is "tanoshuu gozaimashita" (which comes from tanoshiku gozaimashita), but even then it seems to me to be the same form as tanoshikatta if you accept that the latter could've derived from "tanoshiku atta".
I'm not a linguist though, so I do not know if the above ideas are correct, but it's the way I understand Japanese verbs.