The "Starting a dismounted cav" thread partly ended up as a "What's the proper way to use skirmishers" thread.
It has always struck me that, if cavalry was present, and unless the opportunity to make a true, mounted cavalry charge was available, or they decided to withdraw fairly quickly, they would dismount, leave the #4's with the horses, and fight in loose order, similar to infantry skirmishers.
If and when infantry support became available, the cavalry would ultimately yield the field to the infantry, who would then throw out their own skirmish line, with each company/regiment/brigade using its own sub-units across its own front, according to how large the main formation was.
I am not familiar with any cases of an infantry company/regiment/brigade keeping its own men all back in line and relying on cavalry, either dismounted (having horses) or unmounted (not having any horses) as its main skirmish line.
Have I missed something?
It would seem reasonable that an infantry formation would choose to rely on its own men to ultimately form that skirmish line, as the officers know each other and have fought together, rather than to rely upon men from a different branch with whom they may not be as familiar in how they operate.
Specific to reenacting, it has been my experience that dismounted cavalry units tend to be somewhat fewer in number, and with smaller numbers of men per unit, than are infantry units, and are armed differently than most infantry units, making it harder to consolidate either into an infantry unit or as their own, larger unit able to take its place on the battle line.
That would seem to me to be the main reasons why at reenactments they are generally relegated to early skirmish line work, or shunted off to the flanks (both of which, ironically, seem to be main functions of cavalry in reality: Hold the line 'til the infantry shows up, and guard the flanks of the line of battle).