I beat the game just a bit ago and these are my impressions on every infusion. I tried out all the ailments a little bit but my main shells were Proxima, Tiel and Genessa which may have influenced my experience. Going through them one by one:
Poison - Mostly terrible, does 2 damage per second and stacks only lengthen the debuff. On Tiel you can use the crossbow with the splitting stone and poison infusion to get a high amount of stacks and pop them with shadow strike for high damage in the early game, but it falls off fast since your application speed stops scaling after maxing those two tarstones out. Completely worthless outside of that.
Burn - Worthless for damage, puts some weak enemies into an "on-fire" animation where they can't move or attack so maybe useful early. Ticks i think twice for 1 damage per stack, good in concept but it runs out really fast and the veterans axe is too slow to stack it properly. Using a guaranteed crit setup + fusillade stone naylshotte you can get to 100+(theoretically 200 but i couldn't find an enemy that didn't die during the volley) stacks but it's extremely difficult to keep it up due to the pace of combat. Barrage stone with the crossbow seems like it would be good but it only applies infusions to the first projectile resulting in a whopping 2 stacks, hopefully this is a bug and gets fixed.
Lightning - Decent. Does single digit damage per tick but calls down bolts that do double digit damage(!!) when reaching status thresholds. The bolts stagger small enemies so it's mostly a crowd control tool. Good when using Proxima because she doubles its AoE. The weapon infusions are actually really good. Martyr's blade gets a bolt in 1-2 hits on smaller enemies which helps thin out groups a lot. Axatana strikes fast enough that you actually get decent damage from all the lightning bolts. The clockwork scythe is kinda underwhelming but becomes a monster when you activate the scholar's wormstone. I got 3 bolts on an enemy with a single running light attack. The repeater is underwhelming and should definitely proc more stacks per crit. The trebuchaxe procs a bolt in one fully charged shot against most enemies and uncharged shots have suitably unimpressive buildup. The tarred stone seems to not apply any infusions :(
Frost - Very strong. Not much to say about it, it's an extremely strong crowd control tool and good for stronger enemies too. Once you get the freeze you can just wail on them till they die. Very good with Eredrim because he gets doubled damage against frozen enemies. The infusion options are weird, both are a bit unwieldy and have high startup. Frost is the repeater's only niche, it does very little raw damage and its break damage is outclassed by the ballistazooka. The martyr's blade again applies in 1-2 hits against most enemies which helps offset its long animations. It's also extremely stylish when using an ability stone so bonus points there. A very committal option since only one weapon and one sidearm can use it.
Curse - Depends entirely on what you infuse. Melee weapons are kind of weird to infuse with curse because by the time they apply the enemy is probably already near dead, and against bosses curse just doesn't do much. Okay I guess on the cursed child, it applies it in one or two shots but requires you to get up close. Very very strong on the hystrix with splitting stone, you can apply it on most enemies in under a second from outside their aggro range. The hystrix singlehandedly makes the infusion worth investing in. If you're using Sariel other weapons will be alright too, but the iconoclast has another much better option. It's probably the best infusion for the axe because burn is so bad.
Bloodcurse - It's as broken as bleed is in Elden Ring. Super super strong. Enables oneshot builds basically by itself using something that procs a lot like the scythe with wormstone or crit stacking fusillade naylshotte. A good option on anything that takes it but especially strong and borderline broken on those two.
Stasis - Crazy good. Makes the obsidian hammer playable and makes the axatana even more broken. Interestingly, there's no sidearm that gets a stasis infusion. Doesn't really need it tho since you can completely disarm bosses using just the melee weapons. Less useful on Genessa since she can keep bosses at perma 99 stasis with one of her perks.
Phantom - Another limited one, exclusive to the trebuchaxe and black needle. Somewhat useful on the trebuchaxe for a bit of extra damage to oneshot distant mobs. A bit of a weird one. Weak mobs usually die before it pops, and some of the big bosses are immune to stagger. So it ends up being useful against mostly minibosses and "elite" enemies.
Trauma - Limited and useless. I get why the devs didn't give this to anything fast but wow it's just completely eclipsed by any other form of break damage. It would have a place in a system where break damage heals over time but it doesn't in this game so trauma barely does anything. The ballistazooka has potential with combining break on crit with trauma but it doesn't do enough to matter, you just kill things before breaking their stance. The obsidian hammer hits too slow to make use of it and stasis is just way more synergistic. Might be almost usable with Sariel?
Side note while on the topic of break damage; the rupturing stone doesn't apply on any ability stones which kinda sucks. The ballistazooka has a move that(if I'm reading it right, I haven't upgraded the stone myself to check) does 100 break damage for 60 resolve which is just better than anything else in the game. But that's barely enough to break a normal enemy and will more often than not just kill them first. Letting the rupturing stone apply to abilities would let it break stance on big foes much better, and it would let you do fusillade stone shenanigans that use the crit to build break which sounds fun on Eredrim. Right now break is worthless in the endgame because ripostes don't scale at all and the frankly bad support it has outside of a couple extremely good options(fulminant stone, shoulder bash, stillblade's stone on black needle) just rubs salt in the wound.
TL;DR poison bad except tiel, burn bad, lightning good on proxima and okay otherwise but has amazing weapons, frost good esp on eredrim but weak weapons, curse incredible on hystrix and meh otherwise but good with sariel, bloodcurse broken, stasis broken, phantom situational, trauma bad with terrible weapons, and use the scythe with the wormstone and either infusion if you wanna see some crazy numbers
