I certainly appreciate that with an external amp and a unit like a mini-DSP you can tailor the sound, but unless you have enough extra sub that you have no concerns about pushing the limits, there is an added level of security in knowing the internal amp/dsp is selected to drive the sub by designers who are intimately familiar with the details of the driver, port tuning, etc. and that they have tested and proven the components to work well with one another.
When I played the intro to Edge of Tomorrow on dual SUB-1200's at high volume, there was content missing, but the subs never bottomed out and lived on to play another day. If I replaced the internal amp with your "one size fits all" Crown amp, I would not be surprised if the driver got cooked on the spot.
I have no vendetta against externally powered subs, but I think you should consider the specifics of the situation. I do not believe passive subs offer viable competition on a tight budget. It seems you agree with this statement since it was $750 before you suggested a passive option (and that is an in-floor/in-ceiling sub).