Your question can be answered by a detailed study of the Four Noble Truths.
A good overview can be found here and also here.
From the accesstoinsight.org website, you can also read this and this for details.
- The first truth is that there is suffering.
- The second truth is that suffering is caused by craving.
- The third truth is that suffering can be ended by ending craving.
- The fourth truth is that the path to end suffering is the Noble Eightfold Path.
The solution you proposed to end craving, is by extreme asceticism, which the Buddha found did not work. The other extreme end, which is extreme indulgence, also does not work.
So, he discovered the Middle Way of practice between extreme asceticism and extreme indulgence, known as the Noble Eightfold Path.
The main scriptural source for this, is the Discourse on the Setting of the Wheel of Dhamma in Motion.
Within the Noble Eightfold Path, there are 4 levels of training - lay follower of the teachings, the anagarika (sort of a pre-monk), the novice monk or nun, and the fully ordained monk or nun. Each of these 4 levels of training are increasing in degree of intensity but are still within the Middle Way and the Noble Eightfold Path. You can find some details in this answer.
The life of a fully ordained monk or nun is not considered to be one of extreme asceticism, because it does not deny them food, clothing, shelter and companionship.
Regarding guarding the sense doors, the answer comes from the Aparihani Sutta:
"And how does a monk guard the doors to his sense faculties? There is
the case where a monk, on seeing a form with the eye, does not grasp
at any theme or variations by which — if he were to dwell without
restraint over the faculty of the eye — evil, unskillful qualities
such as greed or distress might assail him. He practices with
restraint. He guards the faculty of the eye. He achieves restraint
with regard to the faculty of the eye.
"On hearing a sound with the ear...
"On smelling an aroma with the nose...
"On tasting a flavor with the tongue...
"On feeling a tactile sensation with the body...
"On cognizing an idea with the intellect, he does not grasp at any
theme or variations by which — if he were to dwell without restraint
over the faculty of the intellect — evil, unskillful qualities such as
greed or distress might assail him. He practices with restraint. He
guards the faculty of the intellect. He achieves restraint with regard
to the faculty of the intellect. This is how a monk guards the doors
to his sense faculties.