downside to using a deep cycle battery in passenger car, more specifically as a starting battery, is that it is better suited to providing a low current over long periods of time. Reserve capacity for example, which is 25 amps at 90 or 130 or 180 minutes. The way I understand it is they can do this because their internal plates are thicker. But what happens when it's used as a starting battery and you crank the engine over continuously like 10+ seconds is the battery will internally gas. And that's because of the way the plates are internally. When the battery gives out current the plates inside disintegrate in the electolyte and give off hydrogen/sulfur gas. The gas interferes which the chemical reaction which produces the electricity and the battery will give the appearance it's going dead. You have to let it sit for a minute or two to let the battery stabilize and then it'll seem like it's back at 100%, until you pull large amounts of current out of it again for too long a time. I don't believe it harms the battery at all unless the discharge is so rapid that it causes enough heat to damage it. With a "starting" battery, they are able to rapidly discharge, at least for a longer time, without the internal gassing affecting the chemical reaction.
Deep cycles do not NEED to be run all the way down to be recharged. They are however DESIGNED to be drained completely and fully recharged, many times, hence the term deep-cycle. What hurts the battery (any battery) is letting it sit in a discharged state for too long. The internal lead plates that are disintegrated are in a powder form in the electrolyte, fall to the bottom of the battery. Let it sit long enough and that powder material hardens. It's called sulfation. Once hardened the recharging process does not reintegrate that material back into plate form, and the battery loses electrical capacity, eventually becoming a weak battery that goes dead after cranking the starter for more than 5 seconds.
You also mentioned does not like to be left at full charge overnight- this is false. It is good to keep and maintain all batteries at full charge, or at 100%. All batteries internally discharge, so a float charger or maintainer is good.
Disadvantage to a side post terminal battery is that they leak. My acdelco in the '02 camaro had been leaking, and I caught it when I pulled it out of the car to recharge it on my workbench. I replaced it with an optima redtop which is a top post battery but has nicely designed terminals that give you side posts so it can be a drop in replacement. I don't think I'll ever buy another side terminal battery, they all have the potential to leak at the side posts. Inherent design flaw but I guess that's what you sacrifice to be able to get a small battery that'll fit in tighter spaces.