I also had a traumatic EMCS five years ago (and I'm only now brave enough to be having my second child). Prior to that, I actually did experience induced labor for 32 hours. And I experienced having the baby pushed back IN when she couldn't get out. And the docs telling me she was in distress. Watching pulses and BPs drop. I watched the emergency unfold in the ER. I did see her when she was pulled out, but I was so sick and in so much pain, all I could manage was a half smile as they rushed her out to NICU and knocked me out under general before a transfusion from blood loss. I didn't see my baby for 2 days after that, and I laid alone in ICU. Didn't get to hold her or feed her. And in recovery, they insisted on keeping her in the nursery.
Although I did experience some of the things you say you didn't get to, I do understand where you're coming from. I didn't experience the happy, calm, family-oriented "Yay, I just had a baby!" experience. I fought for 32 hours to give birth to a baby and at the very last second was told I had failed.
This time, the section is planned. Although I still feel sad that I'll never have a baby the "traditional" way, I've gotten over it as I've gotten to watch my happy, healthy little girl grow up. I've realized that it doesn't really matter HOW she got here, but that she did, and that we're both here to enjoy that. I'm glad you came through it all OK. The memory of what you missed will fade over time, when replaced by happy memories.