No, it won't. Not really.
1. Digital filters are still crossovers. Always active (of course), digital, naturally, but still crossovers.
2. Every single dynamic speaker driver already presents a reactive load (mathematically: complex impedance), more precisely an inductive load. Electrostatic loudspeakers represent a mainly capacitive load. Magnetostatic drivers are about the only ones with purely resistive impedance.
A purely inductive load can lead to a lot of heat in the class D amplifier's output filter. Admittedly, this is usually a real problem only with a woofer plus a passive low pass filter. The cure is to apply a digital low pass filter, anyway.
The extinction of passive loudspeakers has been foreseen time an d time again for decades. So far it hasn't happened.
Detrimental effects of passive crossovers are real but usually exaggerated.