Was Martin Luther wrong about baptizing infants?

Toward the end of his life, Martin Luther was extremely critical of the Anabaptists and considered them to be heretics. This inspired terrible treatment of the Anabaptists at the hands of the German princes and rulers of other European countries, both Lutheran and non-Lutheran. I don't claim to be an expert on the Anabaptists, but I do know a bit about Lutheranism and Martin Luther since I was raised as a traditional Lutheran and my grandfather was a Lutheran minister. While there were some suggestions that the Anabaptists were simply too radical for their day, my understanding is that the central disagreement Luther had with the Anabaptists was with regard to baptism as a means of entering into the Christian faith. In fact, Martin Luther and others who would later become devout Anabaptists worked together for a time. The Anabaptists believed that faith demands that a person must make a willful confession of faith to be baptized, and that baptism of infants was not only a bad idea, it was not a sign that a person had chosen to become a follower of Christ. Lutherans, on the other hand (and I don't know how much of this was from Luther himself), believed that a person was Lutheran if they were born to Lutheran parents, so it was okay to baptize infants since it was just confirming what was already in place. I hate to say it, but if this is the true essence of the argument, I must side with the Anabaptists on this one. It seems to me, and again, I am not a Lutheran or Anabaptist scholar, that it is contrary to the notion that one must ask Jesus to enter into their life that an infant could choose to allow Jesus to be their Lord and Savior. Free will demands a choice, and choosing nothing is still a choice. Baptizing babies also seems like a convenient way to make sure that a religion has new followers appearing on a regular basis as a matter of lineage, rather than as a matter of choice. The Anabaptist perspective seems to suggest that they would rather have fewer devout believers than a multitude of "believers" who are only there because their parents brought them to church. As a person who was raised in the Lutheran church and baptized at 6 weeks old (I'm 50 now), I completely get the Anabaptist perspective. I wasn't a good Christian. Even though I was confirmed and attended church every week, I did not have any real faith and I never felt connected to God. It all seemed like something I was supposed to do rather than something I couldn't live without. When I was in my 20s, that all changed. I realized then that I had been ignoring what God was trying to tell me, and I humbly asked Jesus to save me - and he did. I think that is what the Anabaptists were after by objecting to the idea that faith can be inherited. If there are any Lutheran, Amish, and/or Anabaptist scholars out there, can you make the debate between Anabaptists and Lutherans more clear? Because of my youth and how I came to God, it seems like such an obvious thing to me that baptism should be a conscious choice. At the very least, Luther should have been understanding of the reasons why one group might reject the tradition of baptizing infants, and it should have never been allowed to escalate to a matter of such vitriolic contention. On the other hand, requiring people to choose is not a guarantee that their motives are pure. It would encourage people to lie about their faith for status or any number of other reasons that have nothing to do with true devotion to God. And because there are many things that can kill young people, perhaps it is better to be baptize infants. Any thoughts?