I am a father with two small children (around the range to indicated), and I"d argue that introducing them to potential girlfriends early is not really a big deal. They are small, they don"t have a proper reference for relationships. They know what "friends" are, and any girls I introduce will be considered as my friend.
In a few years that will change. They will know what relationships are. They will know about girlfriends and boyfriends, and that a new woman in the house may mean a new person in the household eventually. And they will compare her with their mother. And they will rebel against her on the grounds that she"s not their mother (today, they"d take orders from a girlfriend like they do from any other adult).
And they may get attached to her, and if I dump her they may grieve. And that"s ok and part of life maybe once or twice, but not again and again.
Speaking for myself, it takes months before I know if a girls is LTR/spend-the-rest-of-my-life-with-her material. Until she reaches that stage, she"s a risk to my childrens wellbeing.