More than mechanical challenges (if any) it's actually basic aerodynamics that

makes trailing-edge flaps an (almost) ubiquitous solution vs leading-edge flaps.

From this answer:

The main purpose of a leading edge and/or trailing edge device is to change the camber of the airfoil. Without entering in physical/mathematical details, it can be shown that, going from the leading edge toward the trailing edge of an airfoil, the contribution of each piece of its camber to the aerodynamic force is proportional to the following plot/equation (my own plot of the function $\sqrt{\frac{x}{1-x}}$):

There it can be seen that the contribution to the aerodynamic forces of the forward part of the camber is basically negligible while it is the 30-something% most rearward portion of it which almost entirely contributes to the aerodynamic forces.

  This explains why spoilers, ailerons, rudders, ... whatever surface used to change the aerodynamic forces is placed toward the end of the airfoil and not at its leading edge. This also tells us that any leading edge device like slats does not alter significantly the aerodynamic forces: slats are indeed used to improve/extend stall characteristics at high AoA but have almost no impact on the (slope of the) lift or on the pitching moment (source):

More than mechanical challenges (if any) it's actually basic aerodynamics that

makes trailing-edge flaps an (almost) ubiquitous solution vs leading-edge flaps.

From this answer:

The main purpose of a leading edge and/or trailing edge device is to change the camber of the airfoil. Without entering in physical/mathematical details, it can be shown that, going from the leading edge toward the trailing edge of an airfoil, the contribution of each piece of its camber to the aerodynamic force is proportional to the following plot/equation (my own plot of the function $\sqrt{\frac{x}{1-x}}$):

There it can be seen that the contribution to the aerodynamic forces of the forward part of the camber is basically negligible while it is the 30-something% most rearward portion of it which almost entirely contributes to the aerodynamic forces. This explains why spoilers, ailerons, rudders, ... whatever surface used to change the aerodynamic forces is placed toward the end of the airfoil and not at its leading edge. 

This also tells us that, whatever their name is, any high-lift device placed on the leading edge (like slats or Krüger flaps) does not alter significantly the aerodynamic forces: they are indeed used to improve/extend stall characteristics at high AoA but have almost no impact on the (slope of the) lift or on the pitching moment, as clearly visible in the following plot from this Boeing report:

More than mechanical challenges (if any) is basic aerodynamics that simply

makes trailing-edge flaps an (almost) ubiquitous solution vs leading-edge flaps.

From this answer:

The main purpose of a leading edge and/or trailing edge device is to change the camber of the airfoil. Without entering in physical/mathematical details, it can be shown that, going from the leading edge toward the trailing edge of an airfoil, the contribution of each piece of its camber to the aerodynamic force is proportional to the following plot/equation (my own plot of the function $\sqrt{\frac{x}{1-x}}$):

There it can be seen that the contribution to the aerodynamic forces of the forward part of the camber is basically negligible while it is the 30-something% most rearward portion of it which almost entirely contributes to the aerodynamic forces.

This explains why spoilers, ailerons, rudders, ... whatever surface used to change the aerodynamic forces is placed toward the end of the airfoil and not at its leading edge. This also tells us that any leading edge device like slats does not alter significantly the aerodynamic forces: slats are indeed used to improve/extend stall characteristics at high AoA but have almost no impact on the (slope of the) lift or on the pitching moment (source):

The main idea behind this is that it would be very useful for canard aircraft if deployed on both the main wing and the canard

In a lifting-canard configuration, flaps are only sparingly (or even not at all) used on the main wing because in a lifting-canard configuration the main wing normally lies quite backward and therefore any aerodynamic force created there possesses a big leverarm in respect to the CG: using powerful flaps on the wing would create a lot of pitching moment which should be counteracted by the canard which would then need to be designed bigger/heavier/draggier i.e. the opposite of why a canard design had been chosen in the first place. This is why in a lifting-canard configuration flaps are normally placed only on the canard itself and with fancy constructions.

More than mechanical challenges (if any) it's actually basic aerodynamics that

makes trailing-edge flaps an (almost) ubiquitous solution vs leading-edge flaps.

From this answer:

The main purpose of a leading edge and/or trailing edge device is to change the camber of the airfoil. Without entering in physical/mathematical details, it can be shown that, going from the leading edge toward the trailing edge of an airfoil, the contribution of each piece of its camber to the aerodynamic force is proportional to the following plot/equation (my own plot of the function $\sqrt{\frac{x}{1-x}}$):

There it can be seen that the contribution to the aerodynamic forces of the forward part of the camber is basically negligible while it is the 30-something% most rearward portion of it which almost entirely contributes to the aerodynamic forces.

This explains why spoilers, ailerons, rudders, ... whatever surface used to change the aerodynamic forces is placed toward the end of the airfoil and not at its leading edge. This also tells us that any leading edge device like slats does not alter significantly the aerodynamic forces: slats are indeed used to improve/extend stall characteristics at high AoA but have almost no impact on the (slope of the) lift or on the pitching moment (source):