That’s what I like. 
I’ve never had that problem. 
Many people prefer reflector lights for throwers, and I prefer throwers (with reflectors.) 
I currently avoid TIR lights like the plague. 
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Most reflectors are not particularly tall relative to the diameter, so the spill angle is pretty wide, but there is still a sharp cutoff like you say:
Taller reflectors have a steeper spill angle:
I think a small optical component could be glued to the center of the glass to create diffuse omni-directional spill. This would be worth experimenting with to fine tune the beam of reflector lights.
That’s good. It just shows that we have wildly different preferences. I avoid reflector light like plague and mod any reflector light I have to TIR.
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Yep, different strokes for different folks. 
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This is a really nice idea, I’ve done it with a too throwy TIR. It also occurs naturally on cold days when the water vapor in the reflector chamber condenses in the center of the lens. As long as the diffusion applied does not extend past the truncated center of the reflector, no throw is lost; even a decently bigger diffusion piece results in minimal loss of throw.
I just love TIR optics
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M21H + GT FC40 5000K + 24° or 36° TIR is the perfect neutral & natural light color.
I use it even for one of my fishtanks, because it’s so good.
The TIR gives it just enough of a change to make it better than any reflectorlight that I have or had with the FC40