People did pick a round number when they defined the meter. It was defined so the distance from the equator, through Paris, to the north pole was exactly 10000 meters. They also defined the kilometer, centimeter, and millimeter as round number multiples and fractions of the meter.
Roundness was a theme. The gram is the mass of a cubic centimeter of water. They also defined kilogram, microgram, and so on.
All the roundness was put into the units of measurement. They were tired of units like inches, feet, furlongs, and miles in England, a similar but different system in France, and something else in Germany.
After meters and seconds were defined, the speed of light was measured. It did not turn out to be round.
Over the years, the original definitions turned out to have shortcomings. They were replaced with new definitions. The goal of the new definitions was to match the old ones as closely as possible. The value for any measurement should be the same as closely as possible when using new and old definitions.