Parent's dilemma: restraining

All kids have natural curiosity and often harm themselves in their quest to explore their surroundings. It is not uncommon for kids to drink/bathe from the toilet bowl (after-all it is the only readily accessible source of water). They often crawl under the furniture esp beds & tables and injure themselves when they try to stand up. They unknowingly crawl up the staircase and endanger themselves.
2 weeks ago my kid injured herself by rolling off the bed. My first natural response was to tie chunni (long smooth cloth) at one end of her leg and the other end to a furniture. Ofcourse it was pointed out that I am a horrible parent who is trying to put shackles & leash on the newborn kid. However if I look around:
1. Car seats are nothing but restrains
2. most strollers/prams has belts to tie the kid up (and the belt is made of a much harsh material & confines the movement completely)
3. Cribs with high edges are nothing more than confinement cells for the newborn. the sight of kids holding its vertical bars and peeping outside from the rails gives me that jail feeling.
4. it is not uncommon for people to secure the play-area by a railing.
Before I digress the question is not is it humane to confine the movement of the kid, but how do I do it in a socially acceptable manner? How do I ensure that I prevent my kid from injuring herself, while not being repeatedly reminded of the difference between a pet/slave and one’s own kid.
PS: I have already baby-proofed my apartment & the kid is never left unsupervised, but often this is not enough