Interesting, we have various Dell and Lenovo type-C and thunderbolt docks at work and they can each cross charge the Lenovo and the Dell laptops we have.

Maybe your charger is faulty.

The charger which came with your phone probably doesn't output enough power to charge your phone at its maximum speed, while your laptop's charger has more than enough power for that. But what decides at which speeds to charge is actually your phone's built-in charger (what we are calling a "charger" is actually a power supply, the true charging circuit is always within the phone itself). So if your phone is overheating, either it's just hotter than you expected but still within its design parameters, or your phone charging circuit was badly designed.

> When I plug my laptop in to my phone's rapid-charger, it sometimes trickle-charges and sometimes does nothing.

Even funnier than that: when I plug my phone into my laptop using a USB-C to USB-C cable (because the phone's battery is low and the power is out), the phone tries to charge the laptop; I have to go to the USB control in the phone's notification area and tell it to do the opposite.

That's your phone's fault. It's responsible for protecting itself from excess current.

If it actually overheats and doesn't just get very warm, that's a fire hazard and you are using dangerously faulty equipment.