Well I don't know any caravanners who remove their tow-balls. Certainly none of my friends ever do, yet some of them do have detachables. I have a cover which slips over my tow-ball when not in use, and I put that on as soon as I unhitch. Obviously it doesn't stop me banging my shins, but it does stop me getting greasy. Still, each to their own.
I worked in the caravan industry for years both in repairing and selling caravans and tow bars. Tow bars in the early days were basic engineered from angle iron with a bolt on fixed ball their unsightly appearance resulted in a variety of covers some basic plastic slipover covers or simple egg cup type caps which fell off and festooned the roads and highways. Temporary caps were fashioned from half tennis balls to replace the lost or stolen caps. This led to the popularity of a chrome metal hinge over cover that could not be stolen or lost. Todays modern tow bars are now of such far advanced engineering and designed to fit perfectly. Detachable hitches are locked in place to prevent theft yet detach in seconds to be safely stored to prevent loss. Motor factors and camping shops made a fortune in the past selling telescopic car aerials and loose tow covers.
I think that there is no perfect answer. What suits one person won't suit another. If you are bothered about what others think of the look of your car (I'm not), and you are always going to remove/stow your tow-bar when you unhitch your caravan, then fit a detachable/stowable one. If you probably won't bother removing your tow-ball anyway, fit a fixed one as it's much cheaper. Neither will tow any better, and that's what's important really. It's all simply a matter of personal choice. There is no right or wrong answer.
Requests for Guidance on the pluses and minuses of tow bars has nothing to do with what other people think of your vehicles appearance. The whole point of caravanning is to enjoy travelling exploring new areas and meeting other like minded people. Owners choose and buy Cars, caravans for their own enjoyment and pleasure not caring what others think. Anyone who goes caravanning only to judge the style, type, age,value of outfits or tow bars of fellow campers is sadly missing out. Rest assured the merits of detaching a tow hitch are for the various benefits to the owner not to create any envy from onlookers.