One of the key aspects of the Augustan political system was Augustus letting the Senate feel like they still mattered. This meant not just consulting with senators and letting them manage certain civil administration tasks like the grain supply and the aqueducts, but also assigning senators to important provincial commands where they were in command of troops. Indeed this is one of the reasons we start seeing year long consulships become increasingly rare in the back half of Augustus' reign. Augustus (and his successors) wanted to be able to appoint as many consuls as possible each year, in part because of the political patronage involved but also because they needed more men of proconsular ranks to serve as their legates in the imperial provinces.
Creating a professional officer class would undercut this, since if you have professional officers then there is no reason to appoint senators to command the legions. Thus, creating such a program would be an affront to senatorial dignity and risk undermining the stability of the Principate.
(Also, from the standpoint of the Julio-Claudian emperors having the troops motivated by personal loyalty to the emperor was a feature not a bug of the system, since they were the family to whom the troops were loyal.)
Well if the successor is still Tiberius then it won't actually matter since he'll never spend the extra money or use the extra troops
The stories about orgies probably should be taken with a grain of salt (Claims of sexual depravity were a common feature of Roman political invective.)
Otherwise, while Tiberius was certainly resentful and paranoid in the back half of his reign, I don't think it's fair to say that he went mad. The stories about him being a recluse on Capri are greatly exaggerated as he returned to mainland Italy multiple times during that period. (We know for instance that he came very close to Rome in both 32 and 33 AD). And while Tiberius was rather disengaged in managing the day to day affairs of the empire in the back half of his reign, he was still capable of providing strong, effective leadership in regards to genuine threats to the empire (witness his take down of Sejanus or his response to the financial crisis of 33 AD or his response to the Parthians trying to seize Armenia in 35 AD) or when disaster struck (as seen by his providing succor to the victims of the Fidenae amphitheater collapse (which supposedly saw 50,000 people hurt or killed) and to the victims of the major fires that struck Rome in 27 and 35 AD.)
The political murders are true of course, and are a major black mark on Tiberius' reign, but it's worth remembering that Claudius (supposedly a good emperor) killed pretty much just as many people of senatorial rank as Tiberius did (and this despite Claudius reigning 10 years less than Tiberius). That doesn't excuse Tiberius' murders of course, but it's just a reminder that all of the Julio-Claudian emperors had quite a lot of blood on their hands.
Understandable.