You back up your servers once a week?
I think your 500 mile oil change analogy would be a good answer for “why not keep 30 backups?”, but it doesn’t make sense to me here.
Do you not think that if you’re going to have 5 backups most people would rather have backups every day so that if they do have to revert to a backup they’ve lost no more than a day? The only time I remember an older backup being useful is when images fell out of tombstone.
If they have so little disk space that they can’t hold 5 backups, it would seem better to learn that in 5 days when they still have some memory of what they did than wait 4-5 weeks.