As long as you can meet the minimum spends to qualify for all the bonus miles I don't think your went "too far". I am not sure there is such a thing. :-)

I got several cards back in the March time frame to get in on the AA Visa & Amex, the CO MC, US MC, and then the BA Visa.

Now that the big bonus precedent has been set I think they will keep popping up from time to time. I just worry about first-time cardholder only bonuses becoming the norm.