It's my understanding that mining is in part, the processing of the transaction so if mining ceased altogether the Bitcoins would still exist but you wouldn't be able to use them until someone started mining again. 

IMHO, as long as you can mine on a standard desktop computer you will always have somebody using their office (employers) computer and electricity to mine for "free". I know you can't mine BTC on a standard PC anymore but you can mine XMR and others.

Of course this does nothing for the electrical cost of mining, that is still an issue. I am concerned with the projections that I have seen on the amount of electricity that it will take to mine cryptos in the future. That is something we need to look at. "Save the GPU"