On the 2nd June 260, the puppet Wei Emperor Cao Mao at the age of 20 decided to make a stand against his controller Sima Zhao. Ever since the coup of 249 by Zhao's father Sima Yi, a regent for predecessor Cao Fang against fellow regent Cao Shuang, control had been tightened. An Emperor deposed, imperial family members like Cao Shuang executed, others like Xiahou Xuan (the Xiahou were close kin) kept out of real power, several plots against the Sima's failed.

Cao Mao gathered what attendants and soldiers he could, seven hundred or so, marched against his controller. Sima Zhao was forewarned by some of Cao Mao's close attendants but some of the capital troops under Sima Zhou were unnerved and fled. Sima Zhao's close ally Jia Chong came in with troops, they got unnerved so Jia Chong sent Cheng Ji to charge and kill the Emperor by putting a spear into the imperial body. Cao Mao died and the short coup was over.

It was embarrassing for the Sima's, they tried to scrub the manner of death off the record while at the time they had the Dowager Guo claim Cao Mao was depraved and trying to kill her while shifting blame for the death onto Cheng Ji (who was soon killed) though it haunted their reputation ever since. Cao Mao had made very public his views on his controller, he raised troops and it ended up with him dead while his successor Cao Huan would abdicate to Sima Zhao's son Yan six years later and the Jin dynasty was born.

We do see some of the power that the Emperor still held, troops at the capital became unsettled by the sight of the Son of Heaven taking arms. But Cao Mao was betrayed by some of his close advisers to the powerful controller and his attempt died quickly with his death. His public view of the situation he was in was not enough to sway the court and all the troops to his side, Sima partisans led by Jia Chong held sway.

Emperors sometimes did express their displeasure in open court, Han Emperor Zhi ended up dead possibly killed by Liang Ji after his comment about "an over-bearing General". Last Han Emperor Xian once rebuked his controller Cao Cao "If you are able to assist me, then be generous; if not, be kind enough to release me.” but nothing came of it other then Cao Cao avoided a direct audience after that. Both controllers were, though in power via different circumstances (Liang Ji via the usual regency, Cao Cao by taking in the Emperor during the civil war of the three kingdoms)

The power of an Emperor could, in the right circumstances, like Emperor Huan of the Han overthrowing possible regicide Liang Ji in 159, help lead to the collapse of a controller but the Son of Heaven's power had limits.

In the three kingdoms, Emperor Xian of the Han, Cao Fang and Cao Mao of Wei and Sun Liang of Wu tried to overthrow the powerful controllers, Xian had his wife killed, Cao Fang and Sun Liang ended up deposed with Liang later killed. Even Emperors who were fully grown and in power, their ability to impose their will would indeed be powerful but it would vary depending on the power of the central state, on what condition the Empire was in and how willing powerful factions were to obey, it was not absolute.

In a regency, the Emperor either was too young to rule when father died or had been carefully selected by the Dowager (with an eye on remaining Dowager and in power for a fair bit of time). During that time of growing up, getting a strong education, you are not going to have a chance to build strong connections outside the inner palace. Eunuchs may become your allies (though Dowager can control which ones serve you) but in court, will need more than that.

Meanwhile, the regent, of an important family (in the Han, the relatives of the Dowager, in others powerful officials), a well-established figure (or at least from well-established family) before regency is putting relatives and allies in key positions, building support and patronage. The court knows him, the key positions of the administration and the capital army are under the regent control. The regent and or the Dowager (depending on the dynamic) has a chance to prove themselves as stable, skilled rulers who can manage the dynasty onto good things, winning lots of support.

The Emperor gets older and is in court more. A court filled with the allies of the controller, any group he meets for study and scholarly circles will be carefully controlled, the Dowager and/or the Regent still recognized as the voice in charge. The one you need to get onside if you want a favour or who could destroy you is the controller, not the Emperor. The Emperor is an untested quantity, the regency/Dowager is a known one and if doing a good job, why change it?

If the Emperor stands up in that court and declares treason against the regent, the Dowager could just override the Emperor and as a filial son, the Emperor would have to obey. Even if no Dowager, the Secretariat, the guards, the Emperor could need to carry out the orders to execute may well all be with the controller. How sure is the Emperor that the regent's clients and officers will switch to his side just because the Emperor declares treason?

Emperors did sometimes try to seize power against their controller, using what allies they could build up within the palace, trying to move quickly to seize control of troops and the secretariat, using their authority as an Emperor to take control. It depends on the skill of the plotters to carry the plot out with speed and secrecy, also the situation of the dynasty and the regent.

If the regent was unpopular, divisive or hadn't taken real control of the troops (which was quite often for a Han regent), the regent position could collapse quickly as the important positions were seized, troops gathered and the personal authority of an old dynasty used. Once a coup was underway, people could be reluctant to oppose the Son of Heaven (particularly if he was winning) though as Cao Mao found out, not always. Too many might have their own powers vested in the regime as it is or, if the regent is able to respond strongly, will not make a stand for the Son of Heaven.