I have had several USB PATA readers, including those little "puck" designs that just plug straight into the back of the drive. Very handy with laptop drives as they provide all the power necessary. I've never had to mess with the jumper settings on the drive unless it was set to slave or some of the older drives that have a "master with slave forced present" setting. Understandably, those needed to be changed to master or cable select as it makes little sense to have a "slave" without a "master" or a "master with slave present" when there is in fact no slave present. Both cable select and master settings always seemed to work for me, but YMMV of course. There's tons of bridge chips out there, and I'm sure they all have quirks. Not a lot of QA gets done on these cheap consumer devices.
I have no idea what's up with the whole "power the entire system down" thing with a USB adapter. The drive has no idea what's going on with the system. This should all be hidden by USB through the bridge chipset. Again, with so many different ones out there, YMMV. This should apply equally to SATA drives on USB adapters.
Note that you may need to power cycle the USB adapter to get it to initialize and see a PATA drive since hot-detect can be difficult (lack of standardization). The whole "insert a disk into drive X" would be indicative of this.
Now, with native "docks" that actually just pass the IDE bus straight through, yes, you'll probably need to power down when swapping. Native IDE hot-swap support was rather rare and, to my knowledge, never fully standardized anyway. I've done it before, just to see what would happen, but I only ever did it with Linux, and it took some hdparm "magic" to get things into a working state that probably has no analog on Windows.
SATA natively supports hot-swap, though the implementation is left as optional. eSATA relies on it. IIRC, all of the popular SATA 2 (3Gb/sec) and later chipsets support it. Many SATA 1 (1.5Gb/sec) chipsets did not support hot-swap.
SATA disks should not have any concept of "master" or "slave" or "cable select" as SATA is a point-to-point technology. What "SATA Combined Mode" does is make SATA disks appear to the OS in the same "namespace" as PATA disks. In this case, your SATA disk may appear as the "secondary slave", for example, even if you don't have a PATA disk in that position. The BIOS does some tricks to make it so that when the OS accesses the "Secondary Slave" disk, it actually goes out the appropriate SATA port. This is a compatibility trick and isn't required for an OS with native SATA (AHCI) support (which is basically anything newer than WinXP).
Now, old school SCSI had the addresses assigned by jumpers. SCSI 3 allows the controller to enumerate things. Note that SCSI 3 is over a decade old at this point having been superseded by SAS.