As someone that has their own child, now a stepmother to 3 more, and who's experience was actually really positive, wait.
Couple of reasons, from a selfish point of view, dating changes. Once the kids have been met, it's easier for the relationship to slip into functional rather than romantic. While you and the kids are seperate you make the effort into date nights, or couple time. When the kids are part of the mix it's easier to slip into TV nights or nipping to shop etc.
Secondly its a big deal for the kids. Not just the meeting, but if it doesn't work out. You might tend to stay longer in an unhealthy relationship because of the kids or have the guilt if you don't. They're in the middle a lot, even with the bets of intentions it's easy to tread on the other person's toes. Even when all the exes are on friendly terms, it's still awkward at birthdays etc and just being in the same room, if not for the adults, the kids are aware of the initial at least awkwardness.
6 months isn't a long relationship. Yes of course there are the dream couples that fell in love by date 1, married at date 5 and are still happy 40 years later. That's a rarety especially when meeting older with baggage. You don't just have to agree on similar thoughts or values but also parenting styles. I love my OH dearly, he is my world and every year that goes past is better but my god, if I'd been involved in his children there would be a difference ha ha. You have to balance the ' being involved enough and caring' with ' not being involved too much and overstepping'. Some things like toilet flushing and manners were a higher priority for me than OH so that took a bit of getting used to. But when the relationship is a it more time weathered and solid, it's mor 3likely to get through those tricky stages where everyone's trying to find their way.
Anyway, it can and does work and it can be brilliant. My son loves the extension to his family and vice versa, but it takes time