My grasp on economics is thin but I believe this is not true. Let's assume mowing the lawn by a a service cost $200 in capital investment over 10 years and 200$

My grasp on economics is thin but I believe this is not true. Let's assume mowing the lawn by a a service cost $200 in capital investment over 10 years and 200$/year in labor while the robot cost $1000 capital investment also over 10 years. Then you increased the amount of capital going likely abroad by 800$ and freed up 2000$ of labor cost. That means you have 1200$ freed up in investments but lost $2000 in local economic activity. In short, the capital requirements generally go up with automation in the economic benefit is more often abroad (whether that's Germany or China) This completely ignores many migrant workers sending money home.