Honestly, OP, I used to think this too... but actually if you look at pro-lifers' arguments they do not boil down to "the foetus is a person and being alive is better even if they are born into a shitty life, it's better than being dead." That is an argument/moral position, of course, but actually it tends to be a shallowly thought through one, because when you start to dig into the issue and really seriously look at it, it becomes clear that pro-choice is the only morally defensible position, no matter how uncomfortable a person is with abortion, in the end. And it's nothing to do with a foetus "not being a real person" - but it does sort of end up as a useful shorthand.
If you genuinely believe that abortions should be reduced/avoided you have to look at the reasons that women choose abortion, but pro-lifers are almost never willing to do this. In fact you get all kinds of complicated mental gymnastics like "My abortion is the only moral abortion" when people stick stubbornly to a viewpoint without being willing to explore what it actually means that they are saying.
It's important to look at why because making something illegal doesn't make it magically go away; you can't reduce something without working out why it's happening. And the funny thing is that when you look at why, you find out that the vast majority of women who choose abortion are distressed by this choice and feel that it's something that ideally they would not like to do but that they have no better options. Most individual abortion stories, the average person would read and agree "It was the only possible choice she had". It's not something that people choose lightly, it's something they turn to when they are desperate. So to reduce abortion the most effective tactics are to reduce the number of women in the situation where they feel it's the only solution - increase access to birth control and education as to how it works, increase benefits for parents particularly single mothers, toughen up on rape and/or completely overhaul how rape complaints are dealt with, toughen up on abusive relationships, stop teaching young girls that coercive relationship behaviours are "sexy", toughen down family courts so that abusers can't gain such easy contact with their children, massively increase financial and practical support for families with disabled children and completely change how disabled people are seen within society. None of this is easy, much of it is impossible but some of it is doable or at least possible to make progress towards. And logically, you'd expect pro-life people, if they genuinely believe that a foetus's life is the important part of abortion, would be open to solutions that make women feel more positive about the choice to keep their baby or that didn't cause that life to be created in the first place. Many women choose abortion because they genuinely believe that not being born is a better solution for that potential baby than for them to have the life they believe they can provide. It's not always because they don't want the responsibility.
However, again, what you usually find is the mind boggling position that pro-lifers are actively against many of these things - proper birth control and decent financial support for single mothers and conviction for rape and so on. In fact many of them are so against them that they go the opposite way, and want to BAN birth control, cut disability support, etc etc. It's startling because it's so at odds with this viewpoint - that unborn babies' lives are important and we must protect them - that they insist is the number one, the most important point. It's not, it's so clearly not, because they're supporting causes which go directly against this all the time. So in that case the only real conclusion is that they don't really care about saving lives of unborn babies at all - what pro-life is about, is either a completely non thought out viewpoint of "Ooh killing babies is bad." Well, duh. Nobody likes the thought of babies being killed, nobody throws an abortion party. Or it's quite a well thought out and secretive position of wanting to punish women for having sexual agency or daring to have sex outside of a stable marriage (they also never seem to quite believe that well-off married women could possibly seek abortion and instead have all kinds of ideas about the "type" of woman - or girl - who seeks abortion.)
Again even if you have reservations about abortion after a certain amount of time perhaps, it does help to look at the issue in depth, to look for example at the amount of abortions which happen at these gestations, to read personal testimonies of women who have made this decision, whichever way they went in the end. In fact the amount of abortions performed late are extremely small, almost exclusively for medical reasons, when the baby would not survive (or survive for a short time or survive with an extremely poor quality of life) and do have benefits over letting the pregnancy go to term such as a reduced risk of infection or birth injury to the mother, increased pain relief options, less strain on mental health. But most women who find out they are pregnant too late for abortion or whose access to abortion is delayed for whatever reason decide that a late term abortion would be too traumatic to go through with anyway, even if it was legal. Most women already make that decision for themselves, and I can't imagine that it's an easy thing to go through, even if it is considered kinder to the baby. Anybody who does choose that, again, is in a horrible mental place and I don't envy them.
So in the end even if you believe that a foetus is a person and has a right to life, what protection does making abortion illegal afford those foetuses? None, essentially - because women who are desperate and see abortion as their only possible option do desperate things. What little chance you have to influence the decisions of a few also comes at a huge cost - to the women denied abortion, to their families, to their already-born children.
Maybe it's not clear cut but to me I think most people once they logic everything right down in the real world, not simplifying the issue (it IS complex), not looking at fantasy scenarios like unwanted babies being adopted by nice infertile couples and living happily ever after, can see that making abortion illegal might help a few foetuses survive when they might not have but at what cost? Is it not better to, understanding most pregnancies are terminated very early when the choice is available, let women make a safe clean legal choice - and hopefully they don't have to, but if they do feel forced to, isn't it better that they have sanitary and regulated conditions for that decision? It doesn't make any sense to add red tape to the emotive issue of "aborting perfectly healthy babies at 39 weeks" - in reality, that would never happen, because who would?