They could definitely kill the golden goose.
But for the last 20 years, we have had rapid technological change that seems to be continuing (as far as I can tell!) — widespread internet, internet commerce, smart phones, revolution in media delivery, DNA analysis, genetic engineering, manufacturing techniques, drone aircraft, etc.
And we still have competition between nations, which drives technological advances.
It has been objected that upon the abolition of private property, all work will cease, and universal laziness will overtake us.And the commies still deny this to be true, in spite of the massive disaster that abolishing families and colossal welfare programs have been.