All the elite forces I can think of in modern militarys are some form of special forces, while in, for example, the Napoleonic Wars, Napoleon had 2 types of foot guards, the Old Guard and the Young Guard, and Russia had its own massive lifeguard corps, as did the United Kingdom and virtually every country at the time. What happened to 'elite' front line regiments?
101st Airborne, 82nd Airborne, 10th Mountain Division, Marine Recon, Para-Rescue, Air Cav., Royal Marines.. They are there. I'm not super into modern military stuff, but I'd consider these to be "elite" that are not really Special Forces. I suppose it would depend on what we consider elite, what was considered elite then and how their ideas of elite troops compare to what we consider to be elite.