IMHO, only in very select instances. Otherwise, you still are faced with the insurmountable problem that plagued the Confederacy, and that was forage for the horses, and the corresponding loss of true infantry. After all, mounted infantry was only able to put 3/4 of their firepower on the line due to the need for horse holders. Meanwhile, their mounts were consuming forage needed for the artillery and wagon trains.
Mounted troops, whether mounted infantry, artillery, or cavalry took away horses from the more reliable artillery, wagon trains, ambulances, etc. A strict balance was necessary to prevent the Confederacy from eating itself alive with too many horses and not enough infantry.
Somewhere, perhaps Freeman, I read an interesting account of how many wagons it took [and their horses] just to carry feed and forage for the horses in the wagon train.
Additionally, the practice of allowing a trooper who lost his horse to return home or otherwise search for a remount is just another soldier lost.
Mounted infantry under Forrest or even Tom Green was proven to be effective. Not so with most other folks like Morgan or even Wheeler. Look at the TO for East Tenn & SW Virginia and you will marvel at the number of mounted units that usually caused more harm than good.
There is a lost army in the Confederacy waiting to be dismounted, and I enjoy restructuring the orders of battle to demonstrate the potential increase in infantry.
Of course, there will be those who proclaim the superiority of the Confederate cavalry. But that proved to be illusionary after the 2nd year, and its very success early in the war may have led to retaining so many mounted men.
Remember the cavalry brigades that Lee did have at Gettysburg, while Stuart was absent. He didn't trust them to perform Stuart's role and thus they were less effective as mounted men, IMHO, than they could have been as infantry--or even as mounted infantry.
Longstreet sure could have used them as an auxillary infantry force.
There are many such examples, sadly.