Why didn't the Roman Princeps restructure or dismantle the Praetorian Guard?

tl;dr

Why didn't Roman emperors restructure or dismantle the Praetorian Guard?

Several tried. It didn't end well for them. Most paid for the attempt with their lives.

Although most people tend to think of the Praetorians in the context of the Roman Emperor, they had actually existed long before Rome became an empire. During the Roman Republic, generals or magistrates (called "praetors") had groups of soldiers known as Praetorian Cohorts assigned to them.

The number of Praetorians grew considerably during the civil wars that were initiated by Caesar's crossing of the Rubicon. Both Augustus and Mark Antony had several Praetorian Cohorts. When Augustus became emperor, he united the Praetorian Cohorts into the Praetorian Guard. He had learned firsthand the advantages of having a military force that was loyal to him, personally.

Augustus maintained several cohorts in Rome and dispersed the rest to other Italian cities. Their influence grew substantially under Augustus' heir, Tiberius, and his Praetorian Prefect, Sejanus.

When Tiberius retired to Capri in the last decade of his reign, Sejanus became the administrative head of Rome and, effectively, the leader of the empire. Sejanus passed numerous reforms that favouring the Praetorian Guard. In particular, he moved them from the outskirts of Rome into the city itself and built their barracks (the Castra Praetoria) which would become the Praetorian Guard's headquarters for the next three centuries.

From that point, the Praetorian Guard became simply too powerful to challenge by anyone who didn't have an army at their backs. They could make and break emperors. For example, the guard was instrumental in the removal of Gaius (Caligula) in AD 41, and Nero in AD 68.

The case of Gaius is instructive. in 40 AD, Gaius had announced his intention to leave Rome permanently to the senate. He meant to move to Alexandria in Egypt. This move would have removed much of the power and influence of both the senate and the Praetorian Guard. He was murdered the following year, and the Guard proclaimed his uncle Claudius emperor.

As mentioned above, the Praetorians were also instrumental in the overthrow of Nero, who they replaced with Galba. They then turned against Galba, replacing him with Otho. Otho committed suicide after just three months in power and was replaced by Vitellius.

One of Vitellius' first moves as emperor was to disband the Praetorian Guard. He also had more than 100 of them executed for their role in the murder of Galba. Vitellius created a new guard comprised of Germanic troops who were loyal to him.

Most of the surviving Praetorians pledged their loyalty to Vespasian. When he became emperor, the Praetorian Guard was restored in order to bring order back to Italy in the aftermath of the "Year of the Four Emperors".

Time and again, the Praetorians would involve themselves in Imperial politics. When the emperor Pertinax decided to reform the Praetorian Guard in 193, on the grounds that it had become too powerful and corrupt, the response of the Guard was to murder the emperor and auction the empire to the highest bidder!

(In case you're interested, Didius Julianus won the auction. He would reign for a whole nine weeks.)

It wasn't until Constantine that Rome had an emperor with the power (and sufficient military force at his back) to disband the Praetorian Guard.

The Guard had sided with Maxentius in the civil war, but he was decisively defeated and killed at the Battle of the Milvian Bridge in 312. Constantine dissolved the Praetorian Guard the following year, symbolically destroying their barracks in Rome and assigning surviving Praetorians to postings in the distant reaches of the empire, far away from the political centre.

Sources

Erdkamp, Paul: A Companion to the Roman Army, Wiley, 2011

Smith, R.E: The Army Reforms of Septimius Severus, Franz Steiner, 1972

Southern, Patricia: The Roman Empire from Severus to Constantine, Routledge, 2015

Southern, Patricia, & Dixon, Karen R: The Late Roman Army, Yale, 1996

Speidel, M.P: Maxentius and His "Equites Singulares" in the Battle at the Milvian Bridge, Classical Antiquity, Vol 5, No 2 (Oct 1986), pp 253-262.