Here is a simple solution that I have thought through and believe would have provided the optimal solution when it came to a combination of weight, power and efficiency.
Instead of doing all this fancy MGU-H generating electricity stuff they could keep the MGU-K and replace the MGU-H with gearing the turbocharger to the crankshaft. I.e. The original turbo compounding idea used in the Wright and a few other engines. The MGU-K can still be powered by a battery but that battery is recharged purely by regenerative braking as it was done previously.
Reasons:
1. You get rid of the inefficiencies associated with converting a mechanical force into electricity so immediately you have an efficiency bonus.
2. Because there is less energy to store as the MGU-K is only powered by electricity from the battery which gets electricity from braking, the battery itself can be made smaller and lighter....and cheaper (ya know, that whole thing that they've been blabbing on about for a while now).
3. It focuses much more on conventional car technology which is far more applicable to the current road car industry.
4. No MGU-H and a less complicated electrical deployment system means its cheaper and lighter (more stuff they've been blabbing on about). Sure you gain some of the weight back through the gearing of the turbocharger to the crankshaft but that is tried and tested technology so wouldn't be expensive to develop and manufacture and wouldn't weigh much.
5. The conditions that F1 cars mostly run (high load and high rpm) is perfect for turbo-compounding. When in the general high power rev range at high load I.e. most of the time, the turbine will recovering exhaust energy and will be putting it right back into the crankshaft.
6. 8 gears is enough that at any part on almost any circuit the car will be in its rev range therefore the compressor will be spinning at a sufficient rpm regardless of throttle load without having MGU-H assistance. This means that lag is pretty much a non-issue. Before somebody says "but that reduces efficiency just remember at present we have to take electricity from a battery (efficiency loss) and turn it back into mechanical energy (more efficiency loss) just to spin the turbocharger. I didn't work out the numbers but I wouldn't be surprised if in a total lap using electrics is less efficient to keep the turbocharger spinning for the low load sections when there isn't much exhaust flow.
7. These new engines have probably been a headache to develop as most of it hasn't been tried before. I'm sure quite a lot of the costs have been pure R&D which were then passed onto the teams (more money blabbing talk)
And lastly the best reason of all No. 8. If it ain't broke, don't fix it.
Thanks for reading and end rant.
Thoughts?