Firstly you will have a high G/S on approach and touchdown which is going to reduce thinking time and probably hurt a lot more.
However, my point here is the need for instant momentum. The second you lose the thrust you will decelerate your G/S.
If order to have a 50 kt IAS in a 10 kt headwind your G/S is 40 kts.
In order to have an IAS of 50 kt with a 10 kt tailwind you would need a 60 kt g/s. Where are you going to get that momentum from?
If your stall speed is 45kt you will have a problem unless you accelerate your G/S.
G/S + W/S = IAS so 40+10=50 but with tailwind 40 + (-10) =30
so you need a G/S of 60kt to fly.
Where are you going to get that increase in momentum in a few seconds with a drag inducing windmilling prop in a 30deg bank turn.....only by pointing AT the ground, who is really going to do that?
An 'aircraft' will fly at zero G/S with a strong enough headwind, I have done it in a C150. However, if that wind suddenly drops to zero or a tailwind it will fall out of the sky. That is why you add a gust factor to the approach speed.
During the turn there is a point where you lose the benefit of yr 10kt H/W with the same or a decreasing G/S. You then (relative to G/S and direction) get wind from behind the wing (with an increasing stall speed power off/ banked attitude etc). But you still have to maintain the G/S IAS differential that keeps you flying.
Yes you will have some G/S increase due to the tailwind but that is not flowing over the wing enough is it until you have a groundspeed as in the example of 60kts.
My point is that you have a continuous acceleration in a turn from upwind to downwind which can only be achieved with a 'pitch steep' descending turn.
Best to land ahead
I would be interested in a discussion about this as there are apparently very different opinions.