The Lebanese Army was prevented from deploying along the border with Israel because of a "lack of national consensus". In plain speak that means Hezbollah's allies, Syria and Iran, did not permit it. Hence Hezbollah had full military and security control in the border regions. Even today when the Israeli airforce strikes the southern suburbs of Beirut where Hezbollah have many of their political and social bureaus no one is allowed in except under escort from Hezbollah.
Indeed Hezbollah fighters can be integrated into the security forces as a short or medium-term solution. That's what happened to the other militias at the end of the war.
It's the old regional power game and Lebanon, unfortunately, has very little say in it.