Rendaku, i.e. the voicing of the initial consonant, happens in the native Japanese words (i.e. not in the Japanese words of Chinese origin), in most cases when they are a part of a compound word and they are not the initial word. This serves indeed to distinguish a sequence of unrelated words from a compound word.

There are exceptions when rendaku does not happen, but typically whenever a word like hashi becomes a part of a compound word it will be voiced to -bashi.

"H" is a special case among the consonants, because in old Japanese it was pronounced as "p", which is why it is voiced as "b". Later, in initial positions the pronunciation was changed to "f" and even later the pronunciation was changed to "h". The "f" pronunciation has been retained only before "u", like in Fuji. In non initial positions, the original "p" has become later "v" and even later "w".

These pronunciation changes happened after the creation of the hiragana and katakana syllabaries, so they were not reflected in writing. The orthographic reform that was forced after WWII has brought the written form of the words closer to the pronunciation, e.g. by writing consistently "w" where it is pronounced so. Before WWII, many words written now with "-wa-" were still written with "-ha-", a spelling that has been preserved now only in the particle "wa" (like the spelling corresponding to the old pronunciation "wo" has been preserved for the particle "o").

While the Japanese orthographic reform had some positive effects, in simplifying a little the Japanese writing, it also had the effect that for someone who knows only the modern written Japanese it is difficult to read the Japanese books published before WWII, where many different kanji are used and also their hiragana transcriptions are different.

I assume that this was actually an effect intended by the American occupation forces, as a similar policy was applied by the Russians in all the territories of the Soviet Union (except the Baltic countries), where they forced the native populations to change their writing systems to the Cyrillic alphabet, in order to make difficult for the younger generations to read anything dating from before the Russian occupation.