Something I noticed a lot over the years is many beginner rigging tutorials will have every bone connected to another bone like a real skeleton, but occassionaly there’s a tutorial where the specifically don’t connect the hip bones to a pelvis bone, and they never mention why.
It’s probably just because it’s easier for beginners to think about the rig as if it was a real life skeleton where every bone is connected to each other. And also with connected bones you cannot accidentally make unnatural deformations, like move the arm, finger or leg away from the body. The parenting logic of bones works so that a bone can be parented into another bone in two ways: connected or keep offset. Connected means that it’s connected to the parent bone, so that it starts at the end of the parent bone and can never move away from it. This will prevent stretching that usually is not wanted. Keep offset means that the child bone will stay in the same position in relation to the parent bone, but it doesn’t need to start from the end of it, and you can move the position of it if you want. This makes it possible to get rid of useless bones on pelvis area and other parts, as you don’t need additional bones between hip bone and thigh bones for deformation. And if you press alt+p you are given an option to unparent or disconnect the bone. Unparent means that the parenting will be undone altogether, so the bone will no longer be connected to the parent nor follow it any more. Disconnect means that the parenting will stay the same, but the bone is not connected to the parent any more, so the parenting relationship will only be changed to keep offset.
The deforming bones in a basic human body are only meant to rotate, not to move. If you use only forward kinematics, all bones should be only rotated. And even if you use inverse kinematics to move hands and feet, the ik bones will move yes, but they are technically just defining the spot that a hand or a leg should reach for by rotating. So the deforming bones will only rotate and not move from their positions in relation to their parent bones. Only face bones and correction bones are an exception to this, as face will stretch and move in multiple ways also in real life, and correction bones are meant to do movements that the basic rig cannot achieve just by bone rotations. And ofc if you want to do cartoony effects like arms stretching etc then you will need to move bones and not just rotate them. And having a rig that doesn’t have the bones connected into each other will make this possible. You will need also other more sophisticated setups to make those effects work well, like stretch to constraints etc. but you get the idea. 
Connected bones are eye candy, and are usually a result of building a skeleton using Blender’s bone extrusion operation. A bone doesn’t have to be visually connected to the parent (like in your pelvis example) to be its child. (and the extra hip bones do not have much use; less bone transforms is actually better for performance). Just parent what you want using Ctrl + P (with Keep Offset setting), and the bones will be in the same hierarchy.
Now about whether skeleton needs to be a single unbroken (from program perspective, not visual) hierarchy, from pelvis to the rest of the bones: it depends on a structure and purpose of the rig. Game engines like Unity might require it. While rigs meant for use inside 3d editors can be non-standard. Like shoulders and pelvis having separate root nodes, and the spine being animated by Spline IK chain stretched between them.