My two story apartment building has gutter downspouting down the four corners that connect underground to 4" black plastic corrugated piping that runs underneath concrete sidewalks & extends about 4-6" into the grassed yard, about 4" deep. Of course, the grass eventually grows over & into the piping, clogging it up & causing a backup in the downspouts & gutters.
Given that mowing is an issue, I thought sinking 5 gallon buckets filled with gravel into the ground at the end of the piping might solve the problem, but thought someone out there might have a better solution.
That will do nothing to solve your stated issue with the pipe filling up from grass roots growing into the holes. The end of the pipe should end into open air, not be buried. If this cannot be done consider a popup drain.