The gemara (Brachos 32) presents two reasons why one is not permitted to say “ad kan tzipor tagiyu rachamecha” in davening – 1) because saying G-d is merciful on birds implies he is less merciful on other creatures, which breeds enmity in creation; 2) because G-d’s commandments are decrees; G-d is not motivated by extrinsic reasons like mercy (see previous posts on this issue. The Midrash sides with the view that mitzvos are given to be merciful, and tosses into this same discussion the commandment not to sacrifice an animal less than a week old and to perform milah only on the eighth day so the animal and baby have a chance to reach full strength.
The Sidduro shel Shabbos (shoresh 4) suggests that the machlokes (Rama/Shach Y.D. 261) of whether a baby who was given a milah before the eighth day needs hatafas dam bris depends on this issue. If the reason for waiting until the eighth day sis simply a gezeirah with no reason, then the preceding days count for nothing. But if the reason for waiting until the eighth day is to be merciful to the baby, if one went ahead and did the milah early there is no reason ex post facto to invalidate the bris. (Litvishe readers, please don’t jump on me too much for posting this : )