What you are describing is what
I and others call a bilaterial hardfork-- where both sides reject the other.
I tried to convince the authors of BIP101 to make their proposal bilateral by requiring the sign bit be set in the version in their blocks (existing nodes require it to be unset). Sadly, the proposals authors were aggressively against this.
The ethereum hardfork was bilateral, probably the only thing they did right-- though it appears to have mostly been an accidental side effect due to the fact that their hardfork was rewriting their mutable state directly.. It has a benefit of being cleaner, but it is laughable to call it a "safe hardfork", because it eliminates only one fairly boring source of risk.
The comparisons so soft-forks do not hold-- normally a softfork does not split the chain at all. And it is safe precisely because any fraying it causes if it causes any is not lasting, and will automatically heal without human intervention or significant disruption.
all the upgraded miners will reject those small blocks produced by the minority miners, and extend the chain with small blocks mined by them, thus orphaning those small blocks
As a result, non-upgraded nodes would incur huge loss and will immediately upgrade to the new version, quickly make the hash rate on the new version almost 100%
It's unfortunate to see this kind of ignorance continue. You're adopting a faulty analysis that comes from 'assuming the existence of a privileged position', why is it that you assume the non-upgraded are incurring a huge loss? By each system's own rules its own chain is valid and the others is invalid in that sense they have equal standing, but one has the moral authority of being first and consistent with the philosophy of robustness against external influence. Because of this it would be more valid to say the interlopers are incurring a huge loss if anyone is.
Consider, the _only_ thing that distinguishes the litecoin blockchain from the bitcoin blockchain is a trivial bilateral hardfork. When litecoin came into being and you were running Bitcoin instead of it-- were you incurring a huge loss? No.
From the perspective of the non-upgraded nodes, the parties with the mutilated protocol simply do not exist. Due to being bilateral, the same is true in the other direction. But none of this creates automatic winners or losers. And in all hardfork scenarios there is plenty of opportunity for everyone to be a loser.