"There are a lot of fish in the pond."
If "たくさんさかな" is now accepted, it maybe shouldn't be. Found this on an online language site forum:
"Okay, now, here’s another tricky thing. たくさん takusan can also be used as an adverb (i.e. “a lot”). In that case, you don’t need の no following たくさん takusan.
Examples: たくさん食べます。Takusan tabemasu. (I eat a lot) たくさん勉強しました。Takusan benkyooshimashita. (I studied a lot.)
It’s interesting how たくさんtakusan and the english “a lot” is similar. In English, you cannot say, “a lot books”. Instead, you say, “a lot of books”. In Japanese too, you cannot say たくさん本 takusan hon. Instead, you say, たくさんの本 takusan no hon. On the other hand, there is no problem saying “I eat a lot” or たくさん食べます Takusan tabemasu."
Actually You can say たくさんさかな without の. I have an old copy of Genki 1 and on page 80 in Chapter 4 they introduce the use of たくさん briefly and they use it without の in the examples. Like たくさんさかな.
So you can use たくさん in many ways and it can be translated as "a lot", "many" or "much" and if you use it similarly to "a lot" then you will need の.
Here's also a link to what seems to be the same explanation as the one I have in the book
It's interesting, I started looking into this further after reading your comment and I'm finding conflicting information; ironically, this includes a 2-year old reddit thread that references finding both of our resources & being confused: https://redd.it/4ux2j2, where the comments appear conflicting.
Another was a stack exchange conversation that included a presumably native speaker (given inconsistencies in their English) saying, "...たくさん本...", but then they later amend the response by saying, "By the way, I should have shown you the sentence like this; 私はとてもたくさん「の」本を持っている, because 本 is noun". https://japanese.stackexchange.com/questions/46677/when-do-i-have-to-use-%e3%81%9f%e3%81%8f%e3%81%95%e3%82%93-and-%e3%81%a8%e3%81%a6%e3%82%82
Another resource essentially suggested that in the case of scenarios like, "たくさんさかながいけにいます", that takusan might be modifying the entire verb-phrase and not just the noun it prepends.
It'd be good to have a native Japanese speaker weigh in on this.
I wouldn't put much faith into random redditor's utterances.
Genki 1 is inarguably one of the best and most commonly used course book for preparing for official Japanese language proficiency tests and this information on the use of this word has not changed since the 1999 edition of the book.
If you google something like "たくさんやさい" or "たくさんさかな" or pair たくさん with any other noun with the quotation marks, you can find a lot of native Japanese using the word like also taught in Genki.