>>am I missing something<<
yes, i think you are, Im sorry, The key point everyone is trying to make is you have probably left this too late. By the time you apply and get a card, you then have to spend and get the miles applied. If they say "spend x in the first three months" the odds are you will have to wait three months for miles to be applied, even if you spend in the first week. You would need to ask them this question.
You then have a challenge of finding an award flight available on your route and date. Remember most airlines only permit a very small number of award seats per flight, and many times these are booked up to a year in advance. You could hit lucky, as some times they are available at short notice, but the odds are very limited.
So if you applied for a card today, I very much doubt you would have it within less than a couple of weeks. You then may need to wait three months until you get your miles, they obviously are trying to stop people applying for cards just to get free miles, at which point you are in early to mid July. You then have to find an awards seat, with the airline your miles apply to, available. You will still have to pay the taxes and possibly even fuel surcharges etc, so count on getting the flight about half price, if you do get it, on a good day.
doable, yep, probable, nope. High chance you will just end up with a card you dont need and several hundred dollars worth of debt on it to pay off and no flight.
Get a card if you need one, the offers are to tempt people to get that card over other cards, but obviously you need to look at the rates and terms etc before deciding the best card for you. Getting a card, just to get a free flight, is really not a great idea, and at this late stage, its even less clever.