A retirement bonus (which is what OASDI is for millions of retired Americans) costs more than a retirement insurance plan, because one gets drawn from by everyone, while the other can simply be denied if it isn't strictly necessary for the person trying to collect the benefit.
A more expensive program requires more tax revenue to administer, revenue that could be used on anything else. Since we haven't had a real national discussion about federal taxes in 30+ years in the US, we now take the spending that would be funded with the tax revenues that could be freed up by a less-expensive implementation of retirement insurance - one that's treated as actual insurance - and instead fund it with deficit spending.
More complexity is what makes programs more expensive to administer, not size. You are suggesting adding significant complexity (actual insurance) to what is currently a relatively simple program.
There are lots of things that make it more complex. For example, actual insurance requires you to continue paying in each year to get a benefit. Currently, I can take a year off from working and it has minimal impact on my SSI benefits (as SSI just takes and average index of your 35 highest earning years).
Social Security has it's own funding stream, a tax on wages earned. It does not add to the deficit or increase borrowing. If the funding dries up, the benefits are reduced. This is the Social Security cliff we hear about all the time.