Arminians like John Wesley have sometimes charged that Calvinism undercuts the motivation to evangelize. I think this charge is half true. It seems to me that evangelism is motivated both by Christ's command to evangelize, and out desire that others be saved.
I see the point of evangelism based on obeying a commandment, predestination or no predestination. What I don't see is why our evangelizing makes any difference with respect to the outcome. If I preach the gospel, then God, before the foundation of the world, sovereignly chose that I would do so. If I fail to preach, then God, before the foundation of the world, sovereignly chose that I would not preach. So my choice affects what God sovereignly chose before the foundation of the world? That's called Molinism, and it's a version of Arminianism.
So I think the motivation based on outcome is dissipated once you accept the idea that you can't change who is and who is not elect. Thank God I'm not a Calvinist, so I can accept the outcome-based motivation as well as the command-based motivation.
Calvinists need not see this as a problem for their view.