The idea of lifting the vitrine (that's the transparent part of the case) off the base in order to get the model out is pretty common. It's not so bad if the case isn't too big.
Come to think of it, the stupidest case I've ever seen was built like that. At the Mariners' Museum there's a model representing the liners President Coolidge and President Hoover. It's on the scale of 1/4" = 1', so it's somewhere between 12 and 15 feet long. The vitrine has a frame of stainless steel. In order to open it, the staff has to bring up two big steel lifting frames from one of the storerooms and screw them to the sides of the bottom of the frame. Then rent a couple of chain hoists. The case gets moved (carefully) around the room until the two hoisting frames are directly in line with one of the steel ceiling beams. Two staff members get on tall ladders and hook the chain hoists to the ceiling beams. Then, with a third person watching from some distance to be sure the vitrine doesn't get tilted, the two guys on the ladders wind up the chain hoists and lift the vitrine off the base. That's the silliest, and scariest, exercise connected with ship models that I've ever heard of. The one time we did it while I was there, the museum director came back from lunch just as we were lowering the vitrine back into place. He took one look at what we were doing, turned three shades of white, and shut himself in his office.
Plexiglas (or acrylic; "Plexiglas" is actually a trade name) and glass both have their advantages and disadvantages.
Advantages of plexiglas:
1. It's easier (for most people) to cut than glass. (The human race is divided into two groups of people: those who find it easy to use a glass cutter and those who don't. I'm in the latter category.) It can be cut either with a table saw or by the "scribe, pray, and crack" method.)
2. Plexiglas is harder to break (and if it does break it won't bust up into model-destroying or human-mutilating slivers).
3. It's relatively easy to glue at the corners, thereby avoiding wood or metal framework around the vitrine. (Some people, including, it seems, the majority of trained exhibition designers nowadays, think such frames are categorically ugly.) You can make joints in plexiglas yourself with a solvent cement. The joints will look slightly grey and probably have tiny bubbles here and there. The case manufacturers have various techniques (involving expensive equipment) to make the joints perfectly clear.
Disadvantages of plexiglas: [See also subfixer's post below.]
1. It's more expensive than glass. (For my little Phantom's case the difference was negligible. The plexiglas to make a case for a 1/96 Constitution probably would cost at least $100 more than the equivalent amount of glass.)
2. Plexiglas is a little bit flexible. It comes in many different thicknesses (the price increasing in direct proportion to the thickness; 1/4" plexiglas costs twice as much per square foot as 1/8" plexiglas). My guess is that if a vitrine for the big Constitution were made of plexiglas less than 1/4" thick, the top would sag in the middle. (For my little Phantom case I used 1/8" plexiglas. A drawback to that is that if the joints in such thin material are made in the corners, those joints will be really weak. That's why that case has a wood frame around the vitrine. If you're going to glue the corners you really shouldn't go under 3/16". I made the vitrine for my scratchbuilt Hancock, about 2' long, out of 3/16" plexiglas, and glued the corners. A joint has opened up a couple of times. That's easy enough to fix, but scary. From now on I either use 1/4" plexiglas or make a wood frame for the vitrine.)
3. Glass is a bit easier to keep clean and shiny, using Windex or something similar. Windex is a mild solvent for plexiglas; if you use it regularly for several months the vitrine will start looking dull and slightly grey. (Use a little dishwashing detergent mixed with a bucket of water instead.)
4. Strange things happen when light - especially sunlight - shines through plexiglas. It would take a physicist to explain exactly why, but UV light (a particularly big component of sunlight) passing through plexiglas generates tiny electrical charges. Those charges are particularly devastating to lead; a piece of lead inside a plexiglas vitrine is likely (though not certain) to develop "lead disease." (That's one reason I never put lead - including lead-based solder - in a model.) It also makes things happen to pieces of thread that aren't firmly secured. And I think it fades paint faster.
The environment in which the case is to live introduces other considerations. A curator at the Franklin Institute Science Museum, in Philadelphia, told me that every case in that institution has to be built to withstand the impact of a five-year-old taking a running dive at it from a distance of twenty feet. At the Mariners' Museum things weren't quite that bad; I don't recall any case being busted by a visitor during the three years I worked there.
Some modelers (and museums) like plexiglas cases; some prefer glass. You pays your money - quite a bit of it if your model's sizable - and you takes your choice.