Grabby kids? Some may be, but it all depends on the circumstances.
Example 1: Ann and Bob marry and have two children. They live to a ripe old age. Bob dies first, Ann dies two years later, without having re-married. Everything is shared between the two children equally. This is what both Ann and Bob wanted.
Example 2: As above, but Ann dies when the children are young. Bob re-marries, new wife is Carol. Bob and Carol are married for 40 years. When Bob dies, Carol inherits everything. When Carol dies, she leaves the whole shebang to Bob's children. This is what Bob wanted.
Example 3: As above, but when Carol dies she leaves the whole shebang to her niece. This is not what Bob wanted, but he didn't leave a will, so Carol can do what she likes.
Example 4: David and Eva marry and have two children. Eva dies after 40 years of marriage and David becomes sole owner of the house and all their savings. David marries again. He dies two years later. Wife #2 inherits his entire estate and the children get nothing. This is not what Eva would have wanted, but neither Eva nor David wrote wills that would have protected the children's interests.
I don't think the kids in examples 1 and 4 are grabby to expect to inherit their parents' estate. In examples 2 and 3, there is an argument for saying that after 40 years of marriage Bob's assets are just as much Carol's as his own, so Carol has a very strong claim on them. However, to cut out Bob's children altogether would seem unfair to most people.