Pros and cons about padding a cryptogram produced with an "additive" operation mode

These days I found myself thinking about the implications of padding or not padding block cipher modes that act like additive stream ciphers (I meant OFB, CTR, GCM etc). Let's call additive modes.

You know, people hooked on crypto tends to be I little bit paranoid... Well, at some point of my ruminations about the pros and cons of padding when using those additive modes, maybe I got found a "cons" that let me a bit intrigated: maybe not padding the cryptogram will offer a shortcut for the cryptoanalyst on excluding all other non additive modes during a brute force or even during any other more sophisticated cryptoanalysis.

Since modern ciphers are constructed in a way that any cryptogram will look like random data. If it was encrypted by using CBC or GCM, in practice, the picked mode will not be recognizable by any statistical or other method if cryptogram was a multiple of the cipher blocksize, right?

My doubt about it is if this aleged "operation mode leaking", in state of art, would be considered a weak point in the whole cryptographic infrastructure. Since cryptographers and cryptoanalysts has a endless fight, if a cryptographer is able to do not provide shortcuts for the cryptoanalyst, would not it be better avoid providing any shortcut for the cryptoanalysis? Let's forget a little Kerckhoffs's principle. Even better, if you can keep secret the key, why not also keep the operation mode in doubt?

Sorry if it sounds a little crazy or paranoid question but I am sure that here will be the only place at the Internet where I could be able to find "paranoids" worried about those more philosophical crypto questions ;)

Thanks in advance!

According to Kerckhoffs' principle, everything about a cryptosystem except for the key(s) should be assumed to be known by the attacker (and the keys should be easily replaceable without invalidating prior security analyses of the system).

This includes the cipher and the mode of operation being used.

If your cryptosystem is secure even against an attacker who knows exactly how it works, then attempting to conceal the mode of operation adds no security. Conversely, if your system's security relies on the attacker not knowing how it works, then you're relying on security through obscurity, and will likely sooner or later find out that the details of its operation that you thought were secret actually aren't (and that, unlike changing a key, you can't easily change them when they're leaked).

Relying on security through obscurity also means that you cannot publish your system design for review by experts, and than even hiring individual crypto experts to review it under an NDA is a security risk. Since most cryptographic vulnerabilities arise from implementation bugs and/or inappropriate design choices, this is a serious problem. It also means that you'll have to keep all software and/or hardware implementations of your cryptosystem closely guarded, as an attacker getting their hands on the system will likely be able to reverse engineer it to find out how it works.