Why are there spelling inconsistencies in Southern European languages? What is the historical origin of this redundancy?

Your question assumes that spelling reform is easy as well as desirable. A brief survey of recent attempts at spelling reform in French and German will show how difficult it is to accomplish even minor changes.

Almost all native speakers learn the standard spelling conventions of their language in their earliest years, and they are very reluctant to change, regardless of what new instructions are issued from on high. Part of this reluctance is due to the belief that "correct" spelling is a mark of education and high culture. Part is due to justifiable laziness, because the main benefit of standardized orthography is to ensure rapid and unambiguous comprehension by readers. Changes to improve "consistency" impose a cost without any benefit to the community of readers and writers.

Take the example of the Chinese government's creation of standard Mandarin (putonghua). The pinyin romanization simplified education and is broadly accepted, because it did not replace anything. Simplified characters (jiantizi) are widely accepted but they continue to provoke controversy, with occasional surges of fashion to revive the use of the complete forms. (Not to mention the continued use of the old characters in HK and Taiwan.). By contrast, the government's attempt to standardize grammar was abandoned after it became obvious that agreement on a single system was impossible.

In short, no one except a fanatic (e.g. Dewey, Shaw) is going to attempt spelling reform. For rich-country governments in particular, spelling reform is a waste of effort because it brings no electoral advantage.

It is all about the spelling conventions in those languages. "Latin does not follow spelling changes" because the alphabet Latin uses was conceived specially for the Latin language, Latin spelling was pretty much phonetic so no spelling adjustments are needed when the form of the word changes.

Spanish and Italian use the Latin alphabet which lacks special letters for some sounds that appeared in those languages after they stemmed from Latin, they are [θ] in Spanish and [tʃ] in Italian in your examples. Instead of introducing new letters for those sounds, the Romance languages adjusted phonetic meaning of the already existing Latin letters to their own needs since those new sounds developed from [k] (Latin letter c) before i and e, so Spanish [θi], [θe] and Italian [tʃi], [tʃe] are written as ci and ce which keeps the reference to the original Latin spelling ci and ce ([ki] and [ke]). Whenever the Spanish [θ] appears in other environments, not before i and e, the spelling has to be adjusted in order to explicitly mark that it is [θ] and not [k], so z is used for [θ] in this case. Similarly, Italian has to insert h to keep the ‘hard’ reading of c as [k] (and g as [g], too).

The Romance languages try to balance between phonetic and historical spelling. Introducing a purely phonetic spelling would weaken the visual connection with the parent Latin language, which those languages are obviously trying to avoid. Introducing a purely morphological spelling (which you seem to advocate) without introducing special letters for the new Romance sounds would result in unpredictable reading rules.

The question of optimizing orthography lies beyond the scope of linguistics, since linguistics studies the objective sides of the language, while orthography is purely subjective, it is just a convention, an agreement which exists during a particular period of time, and changing the spelling of the language will no way change anything in the language itself.