ATX is a specification for the size, shape, and layout of a motherboard, and the design of a power supply. It has nothing to do with the cases, except insofar as the cases have to be designed to accept a motherboard based on the standard in order to be called ATX-compliant.
AGP isn't part of the ATX specification (in fact only PCI and ISA are mentioned in it, and that seems to be only so it specifies what they mean by expansion card), so the space taken up by them is dependent on motherboard makers' designs. Some boards do have a double-spaced AGP slot with a missing PCI slot.
There already are half-height PCI cards and cases that use them, they're just not very wide-spread. The width of the PCI card isn't part of the ATX spec either, I think it's part of the PCI spec There is a definite spec for how wide a half-height card is. There just isn't a wide enough need for half-height cards for most devices. I'm no engineer, but it certainly looks like some PCI devices like upper-end sound cards can't possibly be shrunken down to half the width. Other devices like some TV cards or network cards just need a different slot plate, as they're already half-width. Essentially, the cases already have a spec for half-height devices, but there aren't many of such devices, and that's not a fault of the ATX spec.
The floppy is also not part of the ATX spec, so cases that don't have them can be freely made. But most manufacturers of any moderate size case just put it in there because they'd rather people have it available, rather than have someone complain about it being missing. Very small form factor cases are available without a floppy.
Now, the floppy itself should be gotten rid of and replaced with a more reliable and faster device, which is still COMPATIBLE with the way a floppy controller works. The very most basic functions of the BIOS involve the ISA bus and the floppy controller and a keyboard. The emergency recovery functions of a BIOS, which allow you to flash the BIOS using a floppy in case of a bad flash, depend on the floppy functioning. No floppy means you have to do a hot-swap of the chip itself. The floppy has uses that are still good, but the floppy itself is no longer a good device. And while most of us here know how to make and use a bootable CDROM, the average home user only knows how to use a bootable floppy, so an easy to use, compatible bootable device is needed. If the OS goes to look for a floppy, it should find the device and think it sees a floppy. Not sure how formatting would work in that case though.
A new type of controller needs to be designed which the BIOS can work with as if it were a floppy, so that we get speed, and a reliable device, but still retain the basic functions of the floppy. Alternatively, the BIOS could be redesigned to replace the features that a floppy and the ISA bus provide (for video after a bad flash), using either the PCI bus and the IDE ports, or a new type of device connection. However I think that's asking too much of the BIOS; I don't know just how much complexity they can cram in there, and the ISA bus and floppy and keyboard control is likely the most simple basic system that can be done.
There are changes to the ATX spec that would result in case design changing.
Adding slots to the specification (which calls for 7 now), and then allowing case designers to make a case based on whichever number of slots they want (so you could get like an ATX-7 case, or an ATX-12 case). However, motherboard makers would have to retool, and motherboard costs would go up. Most chipsets only support 5 or 6 PCI slots in the first place, so they'd have to put an extra PCI bridge chip on the board for any more slots. The result would basically be that only expensive boards would have more slots, and cases for that would be expensive too. Given the trend to integration of high-performance components, the need for more slots is generally going down anyway (only dorks like in these forums need more). Of course the addition of more slots gives board makers the chance to provide all 6 PCI slots while still giving the AGP slot a wide berth for airflow. It could even let them leave open slot space above the AGP card to allow for proper mounting of a slot fan to bring fresh air to the CPU.
What case design really needs, and which would require a change to the ATX spec and maybe even others, is standardization of all connectors. Right now the "standard" seems to be that the common colored wire is the ground wire, but too many cases don't perfectly go that way, often with the speaker wires being completely differently colored, and sometimes the power switch cable being completely separate and colored differently. The boards should have the pins more plainly labelled or color coded, and all cases should have wires distinctly and consistently colored or labelled to match.
Also connectors for things like Firewire ports and USB ports needs to be standardized in one final way. Right now a case with USB ports in front may come with a solid block connector, or 9 single pin connectors that you have to sort through, and then figure out what your motherboard's ports have for an arrangement to match them. Firewire ports come in multiple types of connectors. You might have a case with the standard metal connector on the end, or wires ending in single pin connectors that you have to match to the pin layout on the board. On the boards themselves, you may have a rectangular box with pins inside, or you might have a single row of pins with a proprietary connector for the manufacturer's back panel ports.