Yuppers sure do!
For me I think it came from my father. When they would move equipment from one farmers field to another farmers field they would wash the equipment to prevent transporting weeds etc to a new field.
We did the same when I was working in the fields for Green Giant. There was one farmer who personally inspected each and every machine for any signs of plants/weeds etc. If the machine didn't pass his requirements it was re-washed in the road until it did pass his requirements.
I have a friend who had a new lawn installed using sod and the first year was fine but by the second year they had all kinds of weeds, crabgrass etc. They figured that they had been brought in on the mowers that the guy they had hired to mow for them.
With that said, I just like to keep the mower clean.