What is the point of EFC if the family cannot meet it??

Yes, colleges can claim to “meet full need” however they define “need”. See this old thread for examples (not current, but you can get the idea): http://talk.collegeconfidential.com/financial-aid-scholarships/1675058-meet-full-need-schools-can-vary-significantly-in-their-net-prices.html

So it is best not to place too much importance on claims to “meet full need”. Instead, the college’s net price calculator is likely to give you a better idea of what its financial aid may be like for you.