Grounding in transistor circuits
Do I just need to get over this and accept a less-than-ideal world where everything doesn't actually work the way I wish it did?

In short-Yes. But from a technical point of view there are rules to follow, such as NEC and UL guidelines, and for some devices ISO standards come into play.

At least in the USA UL dictates minimum insulation thickness and type for a given voltage, and minimum conductor diameter for a given current AC or DC.

The issue of grounding stands on its own. A general rule of thumb is that UL requires all exposed conductors to be limited to 36 VAC or 48 VDC. This is the limit where a mild "shock" is felt in the fingers or palm of your hand. Double the voltage and the pain and skin damage goes up by a factor of 4.

So any low voltage AC or DC device less then the voltage values I gave does not need an earth ground, even if in a metal chassis. However standard wall outlets pack a lethal punch whether 120 VAC or 230 VAC. Devices that plug into AC outlets with a metal chassis MUST have the chassis earth grounded for safety. Most any kitchen appliance falls into this category.

So called "Double insulated" devices are not earth grounded because they are sealed in a plastic enclosure not easy to break, or use a wall-wart transformer to provide low voltage AC or DC, isolated from the main AC lines by magnetic coupling. Some desktop SMPS supplies that power monitors or printers often have a grounded AC outlet plug and pass this ground connection to the DC output connector so the device, which may have exposed metal, is grounded.