Since the neutral wire and ground wire are connected in the main fuse box then why doesn't some of the returning electricity flow through the ground wire to earth?
Yes and No.
There are two separate systems with "ground wires" in the typical US residential service, the three wire Edison service.
The Grounding Electrode System (GES) consists of ground rods and other grounding electrodes, connected (bonded) by a grounding electrode conductor (GEC) to the neutral at the first means of disconnect.
The Equiment Grounding System (EGS) consists of the equipment ground conductors (EGC's or ground wires) run along with all the feeders and branch circuits in the house. The EGS is also bonded to the neutral at the main bond, nowhere else.
Under normal circumstances, no current flows on the EGS; it does not provide a path back to the neutral at the panel to complete the circuit. Current flows on the EGC when there's a ground fault so that the fault will draw enough current to open the fuse or breaker, clearing the fault.
The GES doesn't carry much current under normal circumstances, but whenever there is current on the neutral, there is some current flowing through the GES, through the ground, through the neutral bond to the ground at the utility pole.
Current doesn't only take the path of least resistance; it takes all paths, with more flowing on low resistance paths, and less flowing on high resistance paths.
Normally the neutral wire has very very little resistance, and the ground has significant resistance, so although they are parallel paths back to the utility transformer, very little current flows in the ground, almost all flows through the service neutral conductor.
Be clear: electricity wants to return to source, not ground. Human-made electricity wants to return to the supply transformer, generator, or solar panel which made that electricity.
Grasping this concept will make electricity make a lot more sense.
Nature-made electricity (lightning and ESD) wants to return to its source, which is typically earth.
Since you asked about house wiring...
A lot of novices get excited when they see the Equipotential bond between neutral and ground in the panel. "They are the same thing!" They're not. Neutral is the working conductor, ground (as in the ground wire) is an emergency path. Other reasons too. But relevant to this question is that human-made electricity only has a relationship with earth when we tell it to.
In this case, it's to clamp the potential of our service power to only a few hundred volts away from earth. If it was allowed to "float", as in an isolated system, it could float thousands of volts above natural earth, especially if the supply transformer had a leak. Think about an electric corded lawnmower. It's probably insulated for 600V tops. Keeping power clamped to 120 or 230 volts from earth is quite a safety win.
Equipotential bonding in more than one place creates huge problems, notably with paralleling and unintended current paths in the event of a wire break. Imagine a neutral wire breaks at the panel. Suddenly all neutral current for the whole house comes out to a generator, across its carelessly left on neutral-ground bond, back to the panel, through the panel's N-G bond, and back to source. This fries those wires (neutrals and grounds don't have breakers!) and sets your house on fire. Wire breaks shouldn't do that.
That said, we "do it anyway" between a service (main panel) and its poletop supply transformer. Your house has bonding from N to G to earth. Your transformer has bonding from N to earth. Yes, that is a redundant, parallel path.
Current flows on parallel paths in proportion to their conductance (1/resistance).
So you have a a fat #4 aluminum service drop competing with a bunch of dirt. The dirt's resistance will be quite high but it'll still get a piece of the action. A tiny piece.
But a tiny piece is worth worrying about. Neutral current flow can easily be 20-30 amps. And even 0.1% of that is 20-30 milliamps, which is enough to kick your butt. Stun, and cause a secondary kill via falling or drowning. So treat ground bonds and grounding electrode systems with respect.