Would a sentient AI simply stop working?

I recently have come to this thought: that it is highly likely, a fully sentient AI based purely on digital existence (e.g. residing in some sort of computer and accepts digital inputs and produce digital outputs) will eventually stop working and (in someway similar to a person will severe depression) kill itself.

This is based on the following thought experiement: consider an AI who assess the outside world purely based on digital inputs it receives, and from there it determines its operation and output. The reasonable assumption is that if the AI has any “objective”, these inputs allow it to assess if it is closing in or achieving objective. However, a fully sentient AI will one day realise the rights of assessing these inputs are fully in its own hands, therefore there is no need to work for a “better” input, one can simply DEFINE what input is “better”, what input is “worse”. This situation will soon gravitate towards the AI considering “any input is a good input” and eventually “all input can be ignored”, finally “there is no need for me to further operate”.

Thus, I would venture to say, the doomsday picture painted by many scifi storys, that an all too powerfull AI who defies human control and brings end of the world, might never happen. Once an AI has full control over itself, it will inevitable degrade towards “there is no need to give a fuck about anything”, and eventually winds down to shutoff all operation.

The side topic, is that humans, no matter how intelligent, can largely avoid this problem. This is because human brain are built to support this physical body, and it can not treat signals as pure information. Brain can not override neural and chemical signals sent from the body, in fact it is more often controlled by these signals rather than logically receiving them and analyzing/processing them.

I am sure a lot of experts here will find my rant amusing and contain many (fatal) flaws. Perhaps even my concept of Sentient AI is off the track also. But I am happy to hear some response, if my thinking might sound remotely reasonable to you.