Yes, historically there were only two counters to enemy light infantry. 1) Cavalry and 2) your own light infantry. Cavalry were only viable if the enemy did not have artillery or their own cavalry to drive you off, so most armies employed their own light troops to fend off the enemies. By the end of the Napoleonic war for example every third man in a Prussian Regiment was trained for potential employment in the skirmish line, and Britain had whole regiments and divisions trained for this role.
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