While I've found it handy to have these sorts of characters searchable, I have to agree that having them as "kanji" and their names as "readings" is rather a stretch. 
I guess we need to address △ and friends too.

I agree with Stephen.

I don't think they're useful as dictionary entries. On the contrary, they seem confusing and sometimes plainly incorrect ("仝" as "どうじょう" looks very suspicious).

にょろ is one possible name among many (波線符号, チルダ, 波ダッシュ). GG5 has a 電算俗 tag in its entry for にょろ, so it sounds like it's actually a somewhat slangy name. The wiktionary entry for the symbol doesn't even mention にょろ, but it does say that the symbol is sometimes read as 「から」.

More generally, I don't think it makes sense to have names as "readings" for symbols. For example, we don't have 「🔰」 in a kanji field alongside 初心者マーク. And 「おのづくり」 is a name for the right-sided 斤 radical, but we have 斤旁 as the kanji form and not a 「斤」 symbol.

https://www.edrdg.org/jmwsgi/entr.py?svc=jmdict&sid=&q=2273890
https://www.edrdg.org/jmwsgi/entr.py?svc=jmdict&sid=&q=1000040
etc.

We don't have punctuation characters as "kanji" but we do have several other marks, such as △, 〃, 仝, 々, etc. I think 〜 is much the same as these. They're useful - why strip them out?

Feedback that I received from a user:
https://github.com/stephenmk/Jitendex/discussions/28

He notes that we don't have readings like 「まる」 or 「てん」 on typography 「 。」 or 「、」.

I see there was already a similar discussion in our entry for 中黒 in 2019.

I don't think the symbols belong in the kanji field here. にょろ is not a "reading" for these symbols; it's a name for them.

I've added my IME's default 〜 to a sense note. We probably don't need to display both here.

@@ -4,6 +3,0 @@
-<k_ele>
-<keb>～</keb>
-</k_ele>
-<k_ele>
-<keb>〜</keb>
-</k_ele>
@@ -14,0 +9 @@
+<s_inf>〜</s_inf>