No, but you should get rewarded for what you've done.
For example, if your LS succeded in Breaking the horns off of a Ram HNM, you should get those horns in your loot pool at the moment of breaking, and it shouldn't go to the shell that picked up the fight after you wiped.
They might get that pair of MNK weapons you have a rare chance of getting for defeating the HNM, but your shell got rewarded for what you accomplished.
Also, there could also be a 'Bounty' system in which your Company gains points by going out on bounties for HNMs. Defeating specific HNMs unlocks some of that HNM's native loot pool to be purchased at high cost with bounty points. This way, going out and killing a different HNM even though you have no personal interest in that, awards you points towards a goal you may personally have from a different HNM - even if collecting the points may take a lot longer.
Then you can keep some portion, primarily a consumable item or perk, of the mobs loot pool to be exclusive to them, like a Meteria or a food component. So you have several reasons to hunt down HNMs. Not only are you going for a chance for a quick drop at those U/U items, those that want different items get progress towards them (even if that progress is dirt slow to keep it rare or simply gathering points to purchase an alternative version that may be say a slight lesser to the rare drop.) Meeting conditions in the fight will get you loot as you meet them, so that failed runs aren't completely pointless. And you get the rare consumables that can make the HNM worthwhile to farm even if the power creep surpasses the value of the permanent items that drops. (which could then be used say for Bounty points or GC seals or whatever.)
There are many ways you can impose 'worth' on an item or a monster, and it does not have to just be a super-rare best in slot. And while I agree people have to work for what they achieve, they should be rewarded for the work they have done.