You sound quite sensible - and if you don’t mind me saying so, especially because you’re still pretty young. You’ll get some answers suggesting you’re somehow terrible, but you’re really not. It seems like you do have a realistic perspective on the future, and it’s entirely reasonable of you to want to wait and see.
My child’s father is not on the birth certificate. That was originally for similar logistical reasons - just hadn’t got round to registering the birth, then found out I only had two days left to do it, and he was away with work! And, a while later, we did indeed break up. As a result of him not having that parental responsibility status on the birth certificate, the situation for my child is a lot easier than the children of most of the other separated couples who we know. Some of the fathers do indeed use their ‘rights’ over their children to mess the mothers around and make life awkward for them (especially re holidays, school, etc.).
I’ve had other separated mums express genuine envy when we’ve become close enough for me to share that I’m the only one with parental responsibility. I was originally sad about missing out on getting him on the birth certificate, but I’ve learned so much from other separated mums since then. For example, I don’t have to worry about having my kid’s holiday plans unfairly wrecked; don’t have to beg my ex to agree to the kid’s preferences for school, activities, whatever. Other mums do have to deal with all that and worse, after a separation - and that ongoing source of problems can really have a massive negative impact on the children. The way you’ve described your situation, it seems like your child’s interests might well be best served by the father not being on the birth certificate. Your child’s interests are your most important concern, and that’s what you’re focused on.
So, my advice is stick to your guns, put it to the back of your mind for the time being (there’s no need to even bring it up in conversation with him!), and please don’t feel guilty or bad about it. If you stay together, and if he matures and over time shows himself as being worthy of having parental responsibility for your child, then you can always get around to having the birth certificate amended down the line.
In the meantime, congratulations on your little one, and I hope you’re enjoying all the tiny baby cuddles! x