There are people who make a game of applying for cards as fast as their credit rating will allow (I think 700 is roughly the floor, below which you stop applying).
If the company tries to charge an annual fee, you call them up, try to negotiate out of it, and if they won't, you cancel the card.
Having too many cards isn't that bad of a thing (as long as they are with different issuers). It can be a good thing, because part of your credit score is the amount of credit you are using out of your total credit.
Like everything else, you game your credit score... there is no real value to having it be perfect high, you just need "good", so you get approved.
Also, the miles that are best come from getting new CCs... not from spending. There is usually a minimum spend to get the initial bonus... but after you do that, you can move on to another card, and get far more than $1/mile.
For instance I got a card that gave me 75k miles for $1500 in spending.