I am not a parent, but times have changed in this area, a lot. I also was expected to work and buy myself clothes, etc, though my parents did pay for tuition.  
 

I don't think it's outrageous for him to help his kids, but I'd want to know his plan for helping them become self-sufficient.  

You keep basically asking the same question - which is should your SO continue to support his children after they turn 18? The answer is that given his current financial situation, he should not be supporting his grown children.

The question for you should be why do you want to consider a long term relationship with a man who is not financially stable and has no plans to change his behavior?

HS graduation or turning 18 does not necessarily end a kid's status as a dependent.  My parent supported me until I was 21 though I did work very lucrative summer hobs while in HS and college and even mounted and balanced tires while I was in my first couple of years of college.  At 21 I supported myself though I still lived at my parent's home rent free.  I lived at home for two more years until my XW and I married.  Since then, I have returned to my parent;s home a few times over the years.  My DW, SS and I lived when them for about 6mos while our new home was being built after we sold the first home we bought after we married.  We then returned between international assignments including the entire year of 2017 that my DW lived at my parents while I was on rotational assignment in Saudi.

Dependent status varies by family.  No model is any better than the other and all of them need to be flexible and adaptive to the needs of each young adult kid and the needs of the family.  Some kids need a burning platform to get them to launch, others are very focused on an educational or life goal and need only financial support as they doggedly grind out a degree, a trade qualification, etc...

In my Skids case, he needed a burning platform though his mom and I would have gladly provided him with the parental full ride full meal deal university scholarship anywhere in the world he wanted to attend and could get accepted.  He knew far better than we did that he was not ready to put in the effort.  What he needed from us was a stable base and to keep a fire lit under his feet to get him to step into adulthood.

I send money to my college age son every month and still pay his cell phone. My kid gets scholarship money too so he buys the bulk of his stuff himself.  I think it's reasonable to still support your kids while they are going through higher education. In the end the idea is that they'll be able to get a better job and higher income.  I never got this from my own family but am happy I can help my kids this way.  

The only thing you can control is how you raise your own children. SO will hand OSD everything she wants and she doesn't have to do anything to deserve it other than exist. 

DS does get everything he wants also, but he does all the chores around the house and struggles academically because of a learning disability but is holding good grades. He also does sports as well.

When he turns 14 I am making him work summers at my aunt's farm so he can learn to respect a hard days work. But for every dollar he earns and saves I will match it in an account towards a car when he is 16. 

DS will learn on his own as he has the difference between a kid who is handed everything and one who earns it. SO will never be able to afford to buy SD a car because he doesn't save and spends all his money frivolously on her. She will never work because she is too pampered. She is too lazy to even go to the nurse to get her working papers. 

I don't even see SD getting a lisence because that would require her doing something for herself. 

Everyone rags on YSD but her and I have a good relationship. She respects me and what I do for her. As long as she continues that way I would be willing to help her out. I anticipate she will want to get a job when she is old enough. She is not lazy or pampered.