Lejina is 100% correct, this plan is just setting him up to be even more emotionally invested in this woman... Which I guess is ok, if you really just want to bash Beagle, but the reality is, for men of our age, you don't need to "settle" really, you don't. 75% kids in the u.s. Are being raised by single mothers, MOST of them are tired, overworked, and don't want to deal with shit on a daily basis., want to guess how many of them allow their 9 year old to sleep in bed with them every night? I used to stay up till 4 am playing video games at the age of 12, because my mom didn't limit it, she was going to bars and smoking weed, instead of being an active parent, she figured as long as I wasn't getting in trouble with the law, she must be doing something right, but she was wrong, and it wasn't until I was in my mid 20s that I learned how to temper "most" of my impulses to stay up late even when I know I shouldn't. And lifelong habits are tough to break. And when I went to live with my dad at the age if 13 after my mom lost custody it was an absolute nightmare for me because he was so "unreasonable" for wanting me to be awake and up by noon on the weekends. I'm not saying he did a better job of raising me, but at least he tried in his own misguided way.
The crux of the problem: she doesn't think she is doing harm to her child. She is only agreeing to this because it upsets you. This is going to create additional friction on your relationship with your girlfriend, because if she thought it was a problem, she would have stopped it 6 years ago and with the child as well, because "you" are going to be the bad guy, because the child will know that the mom doesn't really care but is doing it to appease you.
Again, this is only the tip of the iceberg in terms of behavioral problems ahead with this child.
There are MANY many women out there that could use the help of a loving supportive man, to "assist" them in raising their children, not take over, but provide an alternative adult perspective. You deserve better. The child will eventually learn to be self sufficient on his own maybe in his 20s, or never at all, he will not learn it because "mom's boyfriend of a couple months" said so. Trust me, if you want a late 20s or early 30s woman single with a child, it's like shooting fish in a barrel, you don't need to "settle". It's not that you're an "amazing" man, it's that the rest of the men out there are that much worse. If she wasn't dating you, she's likely be spending her nights alone or dating some loser part time drug dealer part time mechanic who once wanted to be an artist, but is currently happy with being assistant manager at Applebee's for the rest of his life.