Let me remind you that, once the main Crhistian army was destroyed at Hattin, Saladin conquered almost all the reign without having to fight a single battle or siege, as all the garrisons were used to made up the army. For instnace, Jerusalem was garrisoned but just two knights, as the the of the troops were with Guy. Runciman in his book "The kingdom of Jerusalem" (vol 2 of his History of the Crusades) goes over this and proves that the Latin inhabitants -and by extension the army- was never enough to colonize the country.
Then could you explain where the troops besieging Acre and garrisoning Tyre come from please?
Runciman's view is (was, sob) simply out of date on this topic. If there was a manpower shortage why did they have such a dense rate of castle construction?