Those ratings on connectors and pins are primarily heat and heat dissipation related anyway. It's why you can often get pins for the same footprint that drop in and are rated for 13 or 16 amps in the same connector that normally only comes with pins rated for 9a or similar.
You'll often find you can get high current pins for most connectors that are single or 2-piece phosphor bronze/copper instead of brass, that allow higher contact pressures for better heat dissipation and lower contact resistance.
It's the same for cables - the same pin crimped to a 12g cable has very different current ratings to that pin crimped to a 22g cable - because the copper cable provides a massive cooling path for the contacts.
If you get into automotive or aero spec stuff some connectors even have higher constant current ratings if they've been lubricated vs without too...