Looking at your list shows the usefulness of armored car/light mech forces in
LW. They are VERY hard to use successfully and really need to be supported by much heavier fire to be made useful on the table against enemy armor. Infantry is also important with light mech force because your main units are easily popped by enemy units. The Luchs and other armored cars are really only capable of resisting basic fire from the front. Enemy infantry move around you and even their rifle stands can ultimately bring you down under weight of fire.
I love armored cars and play them in
EW and
MW all the time. The only times I have tried to use them in
LW has lead to completely wipeage from the table in short order, especially in scenarios that make you split up your force and your lighters just can't hold the line long enough for the rest of your heavy units to come on the table.
In
LW light mech units and recon are best used in support roles to remove concealment bonuses from enemy units for artillery or other units to attack them more easily. They also keep ambushes away from your really important units as well. Once you hit
LW they really don't have the weapons or staying power to be effective as front line forces and as you can see in your own list there you will really be relying on all of the support units to win the battle for you and not the Luchs, so you may as well focus on one of those lists instead.

If you just want to see what it is like to run such a force, by all means give it a go and you'll see how the Luchs don't perform if facing enemy armor.
I do highly recommend a light mech force for the other two war periods, though. In
EW, with most tanks having similar armor levels, the armored cars can be very effective. Heck before the change to the One-man turret rule in the new edition, the French Panhard armored cars worried me more than their tanks did. The panhards could move and still fire their main gun which made them more dangerous and manueverable.
MW isn't too late for armored cars/mech forces either. Until the tigers start appearing late in the period, they can still get the job done pretty effectively.
Skriker