The "bikini cover" is just used when you don't want the sun, pollen, leaves (don't know if will hold up to a "brief" sprinkle)to foul the interior. Used while at work, outing etc. It is opaque and NOT meant to be used while driving (hey, somewhere there's a guy.......)
Assuming you mean the Mopar one, the cockpit cover will hold up to a very, very heavy all-day rainstorm as long as it's properly attached (very taut, with windows up). Mine regularly endures mid-day Florida showers without incident. As long as you keep it well Scotchguarded, you can just carefully lift up one side and let the water run off, and drive away high and dry. (Well, dry anyway.)
The standard soft top folds into three sections and fills about 85% of the trunk. A hard top folded in half wouldn't come close to fitting in the trunk. And as others noted, the hard top is way too heavy for most women to lift by themselves. I prefer to have help if somebody is nearby. It isn't really that heavy to carry, but it's extremely awkward to lift it straight up off the car (or lower it down into position).
The soft top really isn't that bad once you've assembled it a few times, and it's not remotely as heavy as the hard top, although I do think it Mopar did the bare minimum in terms of R&D. A little aluminum and carbon fiber would go a long way towards making it much lighter and more managable, and for the relatively complicated assembly process it still makes a lot of noise at speed unless you remember to cinch up the velcro wraps along the crossmembers.
I was very interested in the prototype lightweight easy-up replacement soft top MadMax (I think?) was describing last year. I guess he never finished, or maybe never went to production.