Wow, you're making this more complicated than it is. The Alternate Function settings allow for many pin/peripheral escape options. These obviously get more restrictive in low pin count devices, where the die may have many pads / "pins" they can only bond out those physically attached to the lead frame in the package. The Data Sheet will provide exhaustive detail as to what can connect to what.
You can "use" PA3, it's just not physically connected to the ST-LINK VCP, and consequently "Doesn't Work" in that use case. CubeMX/IDE may offer PA3 as connected too the USART2 peripheral if it lacks awareness of what the board wiring dictates in this instance.
It's the schematic for the board you said you had, and which I linked too and cited in my response.
Why did they choose PA15 for the UART? I don't know, I suppose PA3 was a better choice for ADC support, but PA2/PA3 are exposed at the connectors, so you could use those for a UART, and perhaps not conflict with the ST-LINK/V2-1 VCP support?
