It makes sense.

The simple answer is that throughout history there have been a number of efforts at spelling/writing reform. This isnt unique to Latinate languages of course; The world's Englishes have likewise undergone the same efforts.

What you see today are varying degrees of conservativeness in the orthographies. So for example nasal codas in French have become nasalised vowels with no coda. However the spelling of French is fairly conservative, so the final <n> is still there. Another example would be French <ç> which is a sort of a compromise. It marks an historical distinction which is no longer retained phonologically.

Imagine you have Latin, and then every X years the spelling of a given offshoot gets its spelling reformed to match up really well with the pronunciation, but they wont all do that at the same time. However they'll all still do it at some point, and since they are all undergoing divergent phonological evolution, even if they reform only very early on, we'll still end up with quite divergent orthographies, especially considering that Spanish and Romanian weren't ever actually identical language varieties. That is to say, they all for the most part started out differing, and only became more so over time.

Im on mobile so no references at the moment but if you want them let me know and i can point you in the right direction. edit: added below.

Further Reading — Romance

Alkire & Rosen (2010) Romance Languages: A Historical Introduction — Specifically Chapter 12. This gives a super short history about the splits, and addresses the point I made that it wasn't Latin one day and then all the child languages on equal footing the next. Super brief. However for a much more in-depth look, see the next one down

• Posner, Rebecca (1996) The Romance Languages — Part of the series of Cambridge Language Surveys. Can't really go wrong here. This gives an account of the language family for someone who is somewhere between layperson and academic linguist. It's not too dry and technical, but still gets to the more academic approach. Later chapters get into the splitting off in more detail. See specifically section 3.4 for information on spelling conventions.

Further Reading — General

• Sebba, Mark (2007) Spelling and Society, published by Cambridge University Press — This is a good overview without sticking to one language. In particluar see chapter 6, Reform or revolution. This has an obviously more sociolinguistic bent to it than just looking at historical developments, but it addresses the big picture well.

• Upward & Davidson (2011) The History of English Spelling — What it looks like. Good overview for English.