Downsides of using a Heavy Guage wire with Low Amperage?
The disadvantages are:

Cost.  Thicker cable costs more for the same length due to using more copper.

Weight.  Thicker cable weighs more for the same length.

More difficult to use.  Thicker cable is less flexible, which also reduces the options where it can be routed.  Very thick cable acts like a heat sink and is difficult to solder.

Less environmentally friendly.  Copper is a non-renewable resource.  The energy to mine it, refine it, form it into wire, and transport it also largely comes from non-renewable sources.  Even if you don't care about the cost, it's still irresponsible to use more of our resources than you really need.