Very good question, which i imagine i will post more about at a later time. 

For starters, the three types of feelings are related to the arising of the three types of defilements, such as explained in <a href="https://suttacentral.net/mn148/en/bodhi#sc30">paragraph 30 of MN 148</a>. Therefore, it appears most essential to highlight the feeling aggregate. As said in <a href="https://suttacentral.net/an3.61/en/bodhi#sc15">paragraph 15 of AN 3.61</a>: 

> Now it is **for one who feels** that I proclaim: ‘This is suffering,’ and
> ‘This is the origin of suffering,’ and ‘This is the cessation of
> suffering,’ and ‘This is the way leading to the cessation of
> suffering.’

As we understand by MN 148, MN 38, MN 37, AN 3.61, etc, feeling can arise *without* there being the arising of craving and suffering. Before the Buddha, I imagine people were seeking a nirvana that was without feeling. Even today on the Buddhist internet, we witness individuals posting obsessively and mistakenly about the cessation of perception & feeling as though it is Nibbana. But the Buddha declared the only possible here-&-now Nibbana and Liberation cannot be without feeling. Therefore, it appears essential to the Buddha-Dhamma, as already explained, to highlight the importance of feeling. 

As for "perception", at least in relation to what is 'supramundane', there are many suttas about perverted perception and enlightened perception, such as <a href="https://suttacentral.net/an4.49/en/thanissaro">AN 4.49</a> and <a href="https://suttacentral.net/an10.60/en/bodhi">AN 10.60</a>. Therefore, it appears to highlight the perception aggregate is also important.