Why shouldn't it be obeyed in iorganic chemistry, as stated in your question. It is quite general for reactions with intermediates and does not exclude inorganic substances.
However, the Hammond's principle is now generally considered obsolete. So, why bother anyhow?
(The principle was generally accepted until the 1970s when too many exceptions started to appear.)
Organic Chemistry is probably easier, but in inorganic chemistry you will learn more. So academically speaking Inorganic Chemistry
there are five branches: inorganic, organic, analytical, physical, and biochemistry. they could be further broken down into sub-branches such as organometallic chemistry, physical organic chemistry, electroanalytical chemistry, and so on and so forth.
analytical, inorganic, organic and physical are the four types of chemistry
Organic chemistry focuses on carbon-based molecular chemistry. Inorganic is everything else. Since organic molecules form the basis for life on our planet, their chemistry is of particular interest and many principles developed in organic chemistry may still be applied to inorganic chemistry.
Organic chemistry is the chemistry of carbon. Inorganic chemistry is everything else, but usually covers metallic complexes.
Organic chemistry and Inorganic chemistry
Carbon: there is carbon present when it is organic chemistry.
Inorganic chemistry. (A few compounds that DO contain carbon are part of inorganic chemistry too.)
Examples: inorganic chemistry, organic chemistry, radiochemistry, biochemistry, electrochemistry, etc.
Inorganic chemistry.
If organic chemistry study the chemistry of carbon compounds the inorganic chemistry stydy the remaining part.
The majority of carbon compounds are studied by organic chemistry.