If you have a controller with "real" RAID (as opposed to "software RAID", "pseudo-raid", etc.) it should be able to transparently mirror drives. The only issue is that it will store some metadata on the drive, making the drives unusable (without extra work) on a controller from a different brand which can be a problem if the controller fails.
The overhead of even pure software RAID (no controller assistance at all) is pretty low on modern hardware - I have some ancient PowerEdge 750s which do OS-based mirroring with no noticeable performance penalty. The only issue is that since the computer's BIOS sees this as two separate drives, if the one that the BIOS boots from fails, you may (depending on the BIOS and drive failure mode) need to swap the drive cables so the system will be able to boot from the good drive. Consider ZFS raidz levels - that is all done in software, but sustained transfer rates measured in gigabytes/second are achievable.
You can't just connect cables together. Take SAS or SATA drives, for example. If you could connect two of them together, what happens when a utility requests SMART data from the drive? Different serial numbers, different statistics. And that's if you could overcome both drives responding at the same time and corrupting the response.
The closest that anything came to this would be
SMD drives, which had a common 60-pin bus cable that was routed through all of the drives and 26-pin data cables which went from the controller to individual drives. But even that required some extra hardware on the controller to perform the mirroring. [The controller did it because in those days the controller had to emulate some manufacturer's subsystem, like a DEC RP06, so it could not act differently from the original.] And you needed 100% error-free packs (very unusual) for it to work. Going back even further, the interfaces were more primitive and more was done in the controller, which is why you couldn't cable the top and bottom of a dual drive like the Diablo 44 together at the head amps.
