Of course, DSP can include EQ and bass controls, not just hall effects. DSP is the best way to achieve the exact sound they're looking for - even the best drivers have some minor dips and peak in frequency response, and mainstream headphones are much worse. DSP would cancel out these deviations from neutrality. However that would mean that unless the headphones come with their own DAC with digital input, they would be converting the analogue signal back into digital for DSP processing, and then back to analogue again - which should degrade sound quality to some extent.
Switchable open/closed could be very problematic as that would result in two completely different sounds - and at best only one mode would sound good. Again, DSP could potentially remedy this.