A 100% effective, low maintenance, reversible birth control method could have an incredible effect on the future of the species. I'm guessing the benefits of fewer unwanted children will be incredible. The possible downsides include a dangerously low birth rate and forced temporary sterilization, but I think the long term effects will be very positive.
You are correct. Except for that part of the population that believes contraception is immoral. Or that rather large part of the population that can't afford the procedure or choose to remain ignorant of even basic contraception. Something like this is certainly more convenient, but ultimately the best method is education.
And since that belief is evolutionarily beneficial, you can see how it would eventually turn into a bigger and bigger problem...