I don't think the GP (Kluny) or GGP (OscarCunningham) disagree with you on that point. If I understand them correctly, it's fine to have unresolved mysteries in your understanding, so long as you are honest about it and explicitly label it[1]. In this case, "hey, we can't quite put infinitesimals on a solid grounding (or Dirac Delta, or whatever), but it doesn't break anything else, so let's see if we can figure it out some other time."

There's a huge difference between "it's not worth our time to resolve this now" and "non-rigorous thought is okay, reality doesn't have to make sense, just do what the high-status people say, they're smarter".

[1] There's a practice in some groups to explicitly say "it works by magic" to avoid false understandings and to flag unresolved issues.