Is a USB charging A-to-C Y-cable a really bad idea?
So one branch could send those signals to a PD charger, VBUS could jump to 20 V, and the other device on the other branch could get fried? Or is that not how USB PD works?
Pretty much. I recall reading somewhere that USB-PD 1.0 was put in the memory hole because RF on the Vbus line could be picked up on an adjacent port making the host think both devices were requesting a voltage increase at the same time. It makes sense but I've been unable to find mention of that to double check.
What about Qualcomm Quick Charge or other such proprietary things?
They do all kinds of crazy things, and some appear to push the limits of sanity and safety. I recall some non-USB protocols putting power on the USB data lines.
I have a charging cable with a USB-A port for the power source and three connections for sinking power. They are micro-B, USB-C, and Apple Lightning. This does not appear to be a passive cable though. It seems to have a small chip in the connector to make sure that the combined load isn't too much for the supply.
I guess the BC1.2 D+ and D- lines might be in conflict, too. Each device would try to measure for the short circuit at the same time, confusing each other?
That's quite possible. The power negotiation assumes no other power draw on the wire. One method used to detect maximum allowed power draw is to increase the current draw until the voltage sags some amount. If there are two devices and both are looking for a safe level of current then both could be varying their current draw, seeing the voltage go up and down, and never settling on a stable point.
If both devices can drive D+/D- then the signals will almost certainly get scrambled. If only one is connected then we get back to one device negotiating power while there is another device taking a nontrivial amount. The source says "I gots 2.4 amps for you!" The connected sink replies, "Okay, I'm taking all 2.4 amps!" Then the other device sees an open circuit on the data lines, a voltage on Vbus, and so assumes a USB-BC compliant charger and starts to draw power. The voltage sags below the allowed limit and both reset. "I gots 2.4 amps for you!" "Okay, I'm taking all 2.4 amps!" Then a reset from a voltage sag. Then, "I gots 2.4 amps for you!"
USB is built to handle some level of bad behavior so this is not likely to cause permanent damage if something is disconnected after a short period. Leaving it this way overnight could mean the devices switching off and on many times quickly for hours could produce enough heat to damage something permanently.
Given that there's solutions for this that would run in the $15 to $50 range I see no reason to hack up USB cables. Hacking up USB cables in general is a bad idea because there are so many useful and safe cables out there that if there isn't a cable for it then it's nearly certain it would be a bad idea to do it. There's many cables and adapters that violate the spec on the market so even if there is a cable for it that doesn't make it a good idea.