As a preface: for the record, I'm pro-choice and I have no intention of convincing you of anything regarding abortion - my goal is point out that we must assume values to even proceed with analysis.
How much should we value a fetus? Why not value potential? Why reject fetal personhood? There's no value-free, scientific answer to these questions. Science cannot define what constitutes a person or when a fetus becomes a person, since these are inherently a value-based questions. A religious document could as arbitrarily say "personhood begins at birth" and then we'd be having the debate in the opposite direction. Science can objectively say when the heart starts beating, when pain first occurs, when consciousness might happen (depending upon our definition of consciousness, which takes yet more assumptions), and so on. It could, theoretically, provide us with infinite facts about the fetus. But not a single fact - nor all of them together - would answer the personhood question. In other words, logic doesn't apply to our initial assumptions. Accepting fetal personhood is neither more logical or less logical than rejecting fetal personhood.
I'll try to point out some value-based assumptions in your response:
but that reasoning can't really be accepted because there are too many unknown variables.
When faced with unknown variables, we should exclude their potential impact from cost-benefit analysis? No degree of precautionary principle? Why not apply a weighted coefficient? How do we decide the weight of that coefficient? 0.1? 0.5? These are all value-based decisions.
no consciousness or ability to feel pain
Why should this our measure?
Do unwanted children on average lead happy lives?
Why should this be a measure? Why consider an unhappy child less valuable than a nonexistant (aborted) child? Let's assume a well-done study shows unhappy children are more economically productive in the long run. How do we sort something like that out? How do we choose between lesser evils?
Are there practical societal benefits to abortions?
How would we measure this? Why choose those measures? Why should we preference the outcome of maximizing one indicator over another? If society were to value the fetus at infinity, then there's no point in even asking this question.
suffering of the mother
How much suffering from the mother is worth it? Why not financially compensate the mother for the predicted disutility she will experience from her unwanted pregnancy? We'll only sort these questions out by examining what we value.
whether or not they have produced or will produce results.
We need to agree on our social objectives in order to determine whether we have results. If our objective is to maximize GDP, that may produce fantastically different results than if our objective is to reduce unwanted pregnancy or to reduce the incidence of abortion. Deciding on any measure takes examination of one's values and an arbitrary decision.
There is a lot of data out there to be gathered, and we've already started doing so and developing algorithms to sort it all out. I'm optimistic and I think it's probable that we will be able to find an approximation of an objectively good value along the way.
Data doesn't ever provide meaning. We use values to find meaning in data. This then informs what's an appropriate measure. How do we even measure harm? Should we evaluate abortion based upon its impact on GDP? Society can, based on some kind of average of values, arrive at some form of an answer for many issues. But if another society - through a different average of values - weights different coefficients slightly differently, why should they not have a different policy?