Phillip:
1. You are correct, of course, that when the user is working with a "raw" HDD or SSD, i.e., the drive is uninstalled in a removable HDD/SSD device that's specifically designed for the drive to be connected to the system while the system is running, the drive should not be connected to the motherboard's SATA data/power connectors (ports) while the system is running. Doing so can be a recipe for corruption/loss of data.
2. However, with respect to our desktop PCs, we work with mobile HDD/SSD racks installed in the case's external 5 1/4" bay(s). The rack's SATA data/power connections have, of course, been connected in the system when the mobile rack is installed. The drive is contained in a removable tray of the mobile rack.
3. As a consequence we frequently have occasion to power-on this or that drive contained in one of the mobile racks installed in the case - we generally work with multiple racks containing a variety of drives - after the system has previously booted. Naturally the drive so powered-on is treated as a secondary drive in the running system. A simple click of the power button is all it takes.
4. As a general proposition we always permanently set the BIOS "hot plug" or "hot swappable" setting to Enable for each SATA data controller, thereby permitting the running system to detect the desired drive "on the fly".
5. Virtually every desktop PC we build for ourselves and others are equipped with multiple mobile racks. I wouldn't be without them and IMO it's a pity more PC users do not so equip their desktop PCs. The cost of such is relatively modest and the advantages of doing so are enormous