It's not impossible. Serious Sam is basically built around the concept of mindless enemies homing in on you in increasingly overwhelming waves.
It works because it pushes out distance in order to give the player time to react, which really is the crux of the matter. So for a start-off you need to re-think your arena design in order to give the gameplay sufficient space to react.
Then there are issues of what I guess amounts to claustrophobia. A swarm of enemies constantly in your face generally translates into a wall of gibs and explosions that fill the frame with visual noise, its kinda wearing and dull. Whereas with a top-down view you can see these waves coalesce into swarms which you then can navigate around the periphery of. This sort of shepherding is something that requires aiming direction/view be separated from movement view/direction...
Sure, "impossible" is too strong a word. My point was trying to merge that style of gameplay with that sort of presentation leads to a series of compromises and trade-offs that dilute the value of both approaches.
Big-time Robotron 2084 fan here from back in the day, so don't get me wrong I fucking love top-down because it gets so much clutter out of the way and allow the gameplay to focus purely on the movement and shooting. My argument is that although FPS have a lot going for them, I feel like they inevitable bring a ton of baggage that stands in the way of that purity.