Even the slightest turn at those speeds moves the airplane by 10s of miles.
Any attempt to intercept or shoot down planes that fast happens at great distances and is totally dependent on computers, radar, and missiles.
> It wouldn't get much time to spy at that speed
That's why you take photos and do the spying part back on base. The SR-71's weapon was its sophisticated camera setup.
> it's fuel limits won't allow great distances without speed changes
When it set its speed record, it crossed from LA to DC on one tank of fuel. (It tanked up immediately after takeoff and immediately before landing, but the cross-country flying part didn't involve a tanker.)