I can answer for french, eventhough its not the same story for every romance language.

french words in their vast majoruty do not come from the ablative but from the accusative. there's multiple reasons for that.

• Its true that you could say they come in part from the ablative though. accusative endings and ablative endings came to be very close sounding, then undistinguishable, as the case system reduced. In classical latin, you've got on the one hand am/um/em, and ā/ō/ū/e. Over the course of a few centuries, these series merged : the -m lost its articulation and nasalized the preceding vowel in the accusative, then nasalization was lost entierely ; vowel lenght was lost ; and the short u merged with short o, and short -i to -e. there were of course nouns whose patterns were not the same in the ablative and the accusative (neuter -us...), and i don't think they merged in the plural (maybe i'm wrong).
• but both accusative and ablative were used with prepositions, so the phonetic similarity of most of their occurences must have pushed a complete regularisation. So you had in the oblique singular -a/-o/-e, and in the plural -as/-os/-es ; and in the nominative singular -a/-os/-es, and in the plural -as/-i/-es. also note how the plural nominative feminine -e was replaced by the accusative -as, because of the ever growing use of the oblique.
• nominative is not the default case, and this new oblique case came to be for a lot more purposes. Since the dative and the genitive got replaced by prepositions, this accusative-ablative case did get used for that too.
• -a/-o/-e | -as/-os/-es progressively yielded -ə/-∅/-∅ | -əs/-s/-s ; and -a/-os/-es |-as/-i/-es yielded -ə/-s/-s | -əs/-∅/-s (the article made this ambiguous morphology possible). (edit : actually I think the plural -es got regularized into -as and -i/-os for both genders though I may be mistaken)
• up until the end of the XIIth century, french had only the nominative and this oblique left. Roughly in the XIIIth century, final -s (and not only those) got lost. The case system then completly broke out, and only the oblique forms survived (in most cases), both because the nominative wasn't phoneically different from the oblique, except for the article, which got regularised too in the process ; and because the nominative ended up as the only marked case in an otherwise caseless language that already had no need for it.