Just to add to the discussion, the best strategy, IMO, is a combination of BPA + need. You shouldn't just draft on BPA, or just draft on need, but what makes the most sense taking both into account.
Then, if the BPA is simply way above and beyond the next prospect you're considering (which would - for argument sake be a 'need') - if it's above and beyond better player, then I would take the BPA. But if the BPA is just so slightly a better 'player' than the 'need', then it makes sense to take player #2.
The draft - just like in real life- isn't just black or just white, there is a lot of grey. It is up to the front office to determine what overall makes the most sense for our football team.
Edit: I also forgot to touch on that position matters, for example, relative value of an elite pass rusher or QB compared to an elite RB, which is valued more in the NFL? This should be taken into account too. You don't want to draft a kicker in the first round even though he is the best player & even if he is 'above and beyond'.