So it may seem odd, chaotic and decentralized to modern people, but Roosevelt's method of forming the Rough Riders (1st Volunteer Cavalry) was perfectly in line with the military tradition of volunteer regiments in America, and before that in Western Europe. The way this typically worked was that the central government issued a call for troops, and locally prominent and wealthy people with political ties to the central government formed regiments locally and placed them under the command of the central government. As a reward, they received military rank and whatever degree of prestige it conferred as well as the possibility of subsequent advancement.

• In 1898 McKinley Issued a call for volunteers and Roosevelt used his prominence and money to raise a regiment, shrewdly making himself it's Lt. Colonel rather than commander.

• In 1861, Lincoln issued a call for volunteers and Dan Sickles, a disgraced NY congressman (and former militia officer), rehabilitated himself by raising 4 or 5 regiments of troops in New York City and being appointed as the commander of one of them, before subsequent promotion. This pattern or similar one was common for nearly all the many volunteer regiments raised by both North and South in the American Civil War. Creating both competent and incompetent Colonels by the bucketful.

• In 1775 the continental Congress issued a call for volunteers, and Daniel Morgan a locally prominent farmer and soldier in the Virginia Shenandoah valley raised a company of riflemen, and then in 1777 a regiment from the same region.

You get the picture, even though I can't think of a famous officer of the War of 1812 who raised volunteers off the top of my head. Indeed George Washington's first real military appointment was to raise a volunteer detachment for the French and Indian war. We could even trace this tradition back to England, and regiments raised by Cromwell, Monck and others in the English Civil War but I'm in danger of straying outside my expertise.

In any case, the central thrust of your question is how did a volunteer regiment in this tradition relate to the central government? The normal thing was that the government issued a call for these regiments, otherwise raising a body of armed men would probably not be tolerated by the government. Then it placed these regiments under the jurisdiction of more senior and hopefully professional military officers, for example the Rough Riders reported to Major General Shafter after travelling to Tampa Bay by rail. These Regiments then began to receive pay, rations and other supplies from the central government. If the Colonel or other officers proved incompetent or politically unacceptable they were not confirmed in command and essentially demoted. Dan Sickles the Civil War officer I referred to earlier was refused position by congress to lead the Regiment he raised initially, although later accepted for such a position. Many Colonels in the Civil War who raised regiments or won elections to Colonel were relieved of command by more senior army officers if they proved incompetent. In short, Volunteer regiments were (at least nominally) entirely under the control and direction of the central government.

Volunteers have never been considered mercenaries (at least no more than other soldiers) due to their strong ties to both the central government and the locality in which they were raised.

Why then did the Volunteer tradition die off? Basically the group of military changes originating in Europe in the late 19th century and culminating in WWI made the system seem amateurish and disorganized by comparison. The Rough Riders are one of the last examples of an effective Volunteer regiment in the old style.