It can actually be argued that they were indeed safer without the Praetorian Guard. I recently wrote a paper on the Roman military system, in which I actually discussed this very issue.

After Constantine abolished the Praetorian Guard and replaced them with the scholae palitinae (literally the Palatine School), no other emperor was assasinated by his personal bodyguard (at least not any that we have a record for). The Praetorians murdered at least five (six if the Tiberius was indeed murdered by his Praetorian Prefect) emperors on their own accord, and in other cases, such as Emperor Galba in 69, they did so at the behest of others. The problem, however, was not just the fact that the Praetorians tended to be in the business of assassinating their own emperors, as the number that they actually killed probably was not extraordinarily high, but also their ability to install new emperors. For instance they of course chose Claudius, whom they believed would be easy to manipulate, after they murdered Caligula and most of the imperial family. Or in the case of Didius Julianus to whom the Guard quite literally sold the Empire.

The Emperor was safer under the protection of the scholae because they were under the direct command of the emperor himself. The Praetorian Guard on the other hand was under the command of two Praetorian Prefects, although it was not uncommon for one prefect to have his colleague killed. This system allowed the prefects to gain too much power and influence among the rest of the Guard. Given the fact that the scholae palitinae did not, at least as far we know, assassinate any emperors, it seems safe to say that they were much more loyal than the Praetorian Guard.

Constantine also decreased the size of the imperial bodyguard to only 500 men. Before this the Praetorian Gaurd had been made up of anywhere from 4,500-15,000 men, the total number differed from emperor to emperor. At its peak strength of 15,000 the Praetorian Guard was effectively its own army, which likely would have made them feel more comfortable with assassinating, and proclaiming new emperors, on their own. The scholae only being 500 strong, however, means that they would have been much less capable of defending themselves in the rest of the Roman army did not agree with their decision to murder the emperor.

In fact it should be noted that Constantine was able to abolish the Guard in the first place, because he defeated them in battle in 312. Falvius Severus had previously attempted to disband the Praetorian Guard a few years before Constantine, but he failed and the Praetorians supported the usurper Maximian. This led to the Battle of the Milvian Bridge in 312, where Constantine's army defeated Maximian, who's army was mostly composed of Praetorian Guardsmen. With this Constantine was able to disband the Gaurd and eventually replace it with the scholae palitinae.

I hope this answer was helpful!