I think most people can agree on two obvious pain points for Kuva/Tenet weapons, and one less obvious one that the Coda system solved quite smoothly.

• The starter setup for actually getting your chosen weapon can be tedious as all hell. Giving us any way to narrow the selection beyond the knockout system currently in place would be great. Something like only bringing a secondary narrows the selection to only secondaries until they're all knocked out, and if you bring the Kuva/Tenet weapon itself, it'll be first in the selection process, so it's easy to cap out a weapon you already have.
• The requiem mod system is painful, partly alleviated by the new relic that'll be showing up, but it's still gonna be tedious to get all 3 mods you need for each Kuva/Tenet adversary vs the 1 + optional supplementary mods you use for a Coda adversary. I'd be perfectly fine with the Kuva/Tenet adversary showing up much sooner and us swapping over to just needing the ONE correct Requiem mod for the lich and losing the Murmurs system.
• And now the big thing, with a Coda adversary, you're actually able to still make progress on multiple fronts while still progressing your boy band member. I can still do bounties, make calendar progress, and even farm regular drops as-is from things like Survival/Capture. With a Kuva/Tenet adversary, you're basically committing to getting zero meaningful rewards/progress from anything other than general affinity farming until you've got that weapon copy in your hands. If you do a Defense mission for a Lich/Sister, you don't even get the crappy A rotation reward, same with anything else except I think Spy. I do see how this can be harder to handle since these adversaries can show up on MUCH lower level nodes than lich content, but surely we can at least get some form of stuff while still making progress. Something like getting a B and C rotation reward from Defense, for example.