When an application you have legally installed on your own computer is communicating with the outside world, it seems a fundamental right to inspect the exchanged data to check that it is not leaking personal information. If the data is encrypted or obfuscated, this could make us suspicious (why hiding if there is nothing to hide ?) and gives additional motivation to audit the security.

Once the api is reverse engineered, we might be tempted to improve the usability of the application by adding some features (scraping all data). If this hurts the server (huge resource consumption), this becomes unethical and may become illegal.

No, but I do personally test the physical security measures of every car or computer I purchase and bring into my home.

It's certainly unintended use of a mobile API, but it's not hacking; it's reverse engineering. HMAC is used for client integrity verification as a signing algorithm; it's not used for generating hashes or ciphertexts of confidential user data. Furthermore, even if it were, it's operating on data that we are sending to the server in the first place. We aren't actually breaking encryption or cracking hashes for confidential user data, we are choosing to manually sign messages to the server using the same methodology as the application itself. Cryptographically speaking there is a very large difference in utility here. The only actual encryption present is the TLS, but both you and the server ultimately see the data.

Reverse engineering occupies a much more ethically and legally grey area than outright hacking because you are fundamentally taking software in your possession and modifying it. There are strong arguments that people should have the right to do this. If can lead to hacking, and it's useful for security research, but it is not in of itself an attack on the application's security (you could make a case that it is an attack on the application's trust model, however).

Now, if the developers relied on the privacy of the API as a form of implicit authorization (i.e. by forging requests from the client I can retrieve another user's data using an insecure direct object reference on a username paramater), and I proceed to do that - yes, that's hacking. You're accessing confidential data in an unauthorized manner, just as you would be if an insecure direct object reference were present on the website. The developers made a mistake in conflating client validation with user authorization, but you've still passed a boundary there.

It is arguable that this is unethical or at least amoral, but if all you're doing is scraping publicly available data using the public mobile API, it is at least legally defensible until the other party sends you a C&D for using their API in an unauthorized manner (so long as you haven't agreed to a TOS by using the mobile API, which really depends on whether and how prominently they have a browserwrap in place). I think the spirit of your point is that someone probably just shouldn't be using an API if they're not authorized to do so, but it's a very important legal and technical distinction to make here that you aren't hacking by reversing the embedded HMAC process.