Realistically, individuals vary greatly from the norm. I've known some 13yo's who were remarkably mature in many ways; I've known 40 year olds who weren't.
However, those are exceptions to the norms, or at least, to expectations. An immature 40yo is a problem; an immature 13yo is common and there are mechanisms in place to moderate their tendency to foolishness (ie parental control, teachers, adult supervision, etc.)
Contrary to societal trends, I raised my son to learn responsibility and to mature much earlier than most; part of this was in how I treated him, tasks I assigned him, and expectations I expressed to him. He was doing work many would consider "adult" at age 13 (running heavy equipment, cutting down trees with a chainsaw, etc.)... but under a certain amount of supervision.
In brief, despite being raised with high expectations of responsibility and maturity and demonstrating far more of same than most his age, no he was NOT a mature adult at 13, and I would have resisted any attempt to make him legally liable for adult responsibilities at that age.
Yes, technically they can reproduce at 13. Mentally, socially, educationally and fiscally they are not ready, and it is parental responsibility to see that it doesn't happen yet.
There's a reason why we use age as the conditional for adulthood, and that is because it is easy to measure, whereas maturity is far more difficult to nail down and not easily tested for.
My son is now 18 and is certainly a man, legally and in his mental and emotional maturity. However I see many of his peers behaving nearly as stupidly as they did at 13-15, and that they are legal adults (more or less) is appalling in some ways... but you have to draw the line somewhere.
Our society has gotten ridiculous in extending adolescent behavior well into the 20s, but legally lowering the age to 13 isn't the answer. Maturity isn't a matter of legality, but of societal expectations and norms, and development.
So no, I'm not in favor of this idea at all. Teenagers can get "emancipated" younger than 18 by court order if they meet certain criteria; this allows the exceptional to do this, and that's good enough, as most are not ready <18.
Possibly we as a society need to recognize that Child/Adult is not a binary state; not On/Off, Yes/No... but rather a sliding scale of development that takes time.
IMHO by the time a child is 13-14yo, they are NOT a "Child" in the same sense as an 8yo is a Child... but they are not an adult yet either. We have this word "Adolescent" for this already.
Even at 18-22 or so, legally young "Adults", there is little question that such persons could (and often do) benefit greatly from some guidance and mentoring by older and more experienced persons.
Hell, practically ANYONE can benefit from some occasional guidance/mentoring by a more experienced person, no? I'm nearly 50, and I miss being able to discuss major decisions with my late father... whether I took his advice or not, he almost always had some interesting points to consider.
Regardless of the law's view, to ME it is something like this:
Baby >5
Child 5-12
Adolescent 13-16 (approx.)
Young Adult 17-22 or so
In my personal viewpoint, and Adolescent is no longer a CHILD per-se, but still well short of responsible adulthood. A Young Adult is technically an adult, but still young enough to NEED (in most cases) some mature guidance in their life.
Possibly our society would benefit from a similar viewpoint being made in law, rather than the current chaotic system where you can be tried as an adult at 12, can have sex legally in some states at 14-16, can't drive until you're 16, can vote or join the army at 18 but can't drink or carry a gun until you're 21... in other words where we make Adult a binary On/Off thing in SOME respects but a sliding scale in others. Maybe we need to officially recognize that it is a sliding scale with several levels and build that into our legal code.