The basketball Cinderellas (which I'll cover in a moment) develop because of two primary notions: 1) 64 (or however many now, 68, whatever) teams make the tournament; 2) lesser-known teams without NBA level talent can get lucky enough that they might have a team that in years three and four of their college careers, teams have played MANY games together and know one another's tendencies and what they do under certain circumstances. They can square off against a Duke or Kentucky that has all those 'one and done' players who are more talented individually but that might lack the team concept.
I think the key difference is the level of financial investment required in order to be competitive. To put together a pretty good basketball team, you need a dozen scholarships, a good coach with a couple assistants, and a gym. It's an order of magnitude more expensive (at least) to build a competitive football team with 85 scholarships, a head coach plus a dozen assistants, and much more in the way of facilities & equipment. Building a playoff-caliber basketball team is well within the reach of hundreds of schools, financially-speaking, which increases the odds of one of them pulling off a successful cinderella season. It's also easier, and less expensive, to maintain a high SOS in basketball, due to the larger number of games and distribution of quality teams across the country. More games means more chances to schedule quality OOC opponents (vs. a max of 4 for football), and more quality teams overall means that the cost of a good SOS is lower in general due to less travel.
