Am I missing something, where are you getting all this from?
From Strategic Operations pages 43-44.
Why would my infantry not have their gear with them in preparation for the drop, and be ready to go immediately?
It depends on whether their living accommodations are configured as the more comfortable steerage quarters (simply living quarters) or the miserable infantry bays (barracks with some room for storing equipment). If you have neither, well, lets just say that you had better be ready for a mutiny.
"Infantry units are treated as cargo of mass equal to an appropriate infantry compartment (see p. 239, TM) because, while the soldiers can walk off a ship quickly, unloading their gear from a cargo bay is a more tedious process than unloading from a real infantry bay or compartment." (SO, p.43)
Would a cargo bay not have a ramp leading into it to ease loading and unloading? If so, why could vehicles not use it to drive into, and out of? I can understand the issue of time in regard to 'Mechs (because from my understanding, they must be transported as prone due to lack of gantries to hold them upright), and flying Vehicles (because a helicopter/VTOL does not take off from inside a hanger, it must move out of the enclosed area first), but the rest makes no sense. Should I not just be able to use the Cargo Carrier rules for loading, and unloading from pg. 261 of TW?
Units transported as cargo can't simply drive off and immediately enter combat like those transported in appropriate bays. Besides being secured for the trip to prevent movement of the units, their turrets, weapons, electronics, etc are also secured to prevent damage to the unit or the DropShip carrying it. After all it would probably not be a good thing if a PPC accidentally discharged in the cargo during reentry. ;)
Not to mention that unlike appropriate transport bays, technicians/mechanics are unable to gain access to the unit and get it ready for combat. All the maintenance, loading of ammunition and other tasks done in transport bays needed to make a unit ready for combat have to wait until after the unit is unloaded when it is transported as cargo. See the rules regarding "Units and Personnel in Cargo Bays" in SO, p.43-44.
Also, since larger and/or heavier items are often transported as cargo (such as 'Mechs) that I would imagine are beyond the scope of the attendant bay personnel to lift, even with the assistance of exoskeletons, should cargo bays aboard DropShips be assumed to have lift hoists?
Cargo bays don't get any bay personnel specifically assigned to load/unload cargo (neither of the two pure cargo carriers - the Buccaneer and the Mule - have any bay personnel). Its the crew that does the loading/unloading and, if available, with the assistance of spaceport ground crews. As far as lift hoists are concerned, yes they do, but those lift hoists are designed for being able to handle large amounts of weight not speed. Even with the assistance of lift hoists there is only so fast a limited number of crew can load/unload a DropShip especially when handling non-standard cargo (cargo not in cargo containers or pallets).