How can you agree lesser included charges are ok but not that they can lead to a mistrial? That doesn't make sense. It's a charge the jury need to evaluate, and if they aren't unanimous you think it should just go away forever?
Yes. For several reasons.
Lesser included should be an option for the jury, but the jury shouldn't be obligated to reach a verdict on them. They should be something that the jury
can reach. Basically the prosecution should only be able to formally bring a single charge for a single given action, and if the defendant is acquitted of that charge and the jury declines to convict on a lesser charge, it's over. It's not "We're charging you for Murder 1 AND Murder 2 AND manslaughter." It's "We're charging you with Murder 1, and the jury can find you guilty of Murder 2 if they so choose."
It would likely have a small deterring effect on over-prosecuting, which I consider a major blight on our nation.
Finally, the prosecution has such a huge advantage that there's some chance a completely innocent person would be wrongly convicted in a second trial. The prosecution gets another shot, a chance to adjust their strategy, tweak their cross-examining, etc. So does the defense, but in most cases the level of resources on each side isn't remotely comparable. Plus the whole "better to let ten guilty go unpunished..." maxim, which I believe is hugely important.
I realize that different people have different notions of justice and that these notions may be even be idiosyncratic. This particular case is so deeply offensive to me that I can't believe so many people could disagree, but here we are.
Probably nothing left for me to really say at this point.
Has this exact legal question ever made it to the Supreme Court? The cases cited so far only concern elements of the question, not this exact one.