What is the origin of the Italian custom of only writing accents over the last vowel of a word?
In general Italian words have kept the accent that had the Latin words of origin.
Some important changes were the followings.
The maintenance of the original position of the accent has not occurred in some compound verbs, in which the phenomenon of recomposition occurred: whenever the basic verb was recognizable, the speakers restored it in its original form and accent: for example in renŏvat, the base verb nŏvat was recognized and we had rinnòva.
In the transition from the perfect (latin) to the passato remoto (italian), in the third person singular we have phenomenons like:
The fall of the output (i) determines, in the perfect of the verbs of the first conjugation, the formation of a secondary diphthong au and then the monophtong [ɔ], whence the final truncated form amò. In the perfect of the fourth conjugation, the same fall of (i) and the passage from the unstressed u to o produce the ending io, with subsequent fall of the final o by analogy with the first conjugation.
The Latin had various alternative forms to the synthetic future. Among these, it was fortunate the form contructed with habeo with the meaning I have to: so for example laudare habeo> laudar(e) * ao> lodarò > loderò. The same for the other persons.
In many words, the apocope by haplology occurred, that is the elimination of a syllable when two consecutive, identical, or similar syllables occur (nu(tri)trix > nutrix).
bon(i)tate(m)>bontate (syncope of the intertonic vowel) > bontade (sonorization of t)
civi(i)tate(m)>cittate (syncope of the intertonic vowel) > cittade (sonorization of t)
virtute(m)>virtute>virtude (sonorization of t)
It was very easy that these words (like many others, on the other hand) were followed by a functional element like the preposition de, ancient variant of di: bontade de Marco, cittade de Roma, virtude de Cristo, etc. Thus, they came to determine the sequences in which there were two consecutive syllables de, the word final and the preposition. This repetition was avoided with the haplological apocope of the first -de: bonta(de) de Marco, citta(de) de Roma, virtu(de) de Cristo, and thus we had bontà, città, virtù.