Don't these things use Gold codes or something similar to eliminate temporal aliasing problems? I guess that wouldn't make multipath issues go away completely, but it could fix the case you're referring to.
You can, and we did an extremely limited form of that — see other comment on reducing correlations. But you have an energy limit from eye safety concerns, so energy spent on spreading the signal over time and modulating it directly takes away from power giving range. And doing non-trivial modulation isn’t easy — most of these pulses are generated by a capacitive discharge, which limits shaping.
You can, and we did an extremely limited form of that — see other comment on reducing correlations. But you have an energy limit from eye safety concerns, so energy spent on spreading the signal over time and modulating it directly takes away from power giving range. And doing non-trivial modulation isn’t easy — most of these pulses are generated by a capacitive discharge, which limits shaping.