If gold gets too valuable relative to labour, more mountains in South America will be pulled down to extract the gold.
Think of the way hundreds of millions of dollars have been put into bitcoin mining ASICS just because someone saw a return could be pulled out if thin air... Gold mining is pulling a return out of rock when the economic conditions are right.
(Technically it will a little until the network difficulty adjusts.)
Sure, mining may increase the supply of gold... a very small amount compared to the existing supply. It's not going to move the needle in terms of supply vs. demand, though.
It can be counterfeited or debased. Will you carry around a scale and testing supplies?