The churgeon may land in my above case (you really have to want an alchemist/healer, because almost any other specialist healer build will probably to the actual job better).
I think part of the problem with the chirurgeon is that magical healing got a huge last-minute boost (by adding +8/spell level to the amount healed by a 2-action
heal, and adding a similar-sized boost to
soothe), and elixirs of life did not keep up. In the playtest, an 8th level cleric would cast a 4th level
heal for 4d8 (average 18) points, and an 8th level alchemist could make an elixir of life healing 7d6 (average 24). That's a comparison that's pretty favorable to the alchemist. But in the published version, the elixir of life is 9th level for starters instead of 8th, and heals 5d6+12 (average 29). That might seem good, but not when compared to a 5th level
heal doing 5d8+40 points (average 62 – twice as much). And that's without considering that alchemists off-load the action cost of their healing on the healed target (when the whole point of having a healer is that the healer spends their actions and resources healing, leaving damage-dealers free to deal damage).
The numerical comparison is a little unfair, because the cleric will likely have something like 3
heals per day, whereas the alchemist can make up to 39 elixirs, although that's assuming they use all their reagents on that. But IME, healing big is more useful than healing efficiently, because when you're not in a hurry you use Treat Wounds instead.
Another chirurgeon problem is that their Perpetual Infusions gets them unlimited antidotes/antiplagues, but (a) an antidote or antiplague already lasts for 6 hours, so you generally don't need all that many of them, and (b) by the time you get them, you should be about to get
resilience runes so they're effectively only +1. I mean, +1 to saves versus poison and disease isn't nothing, but it's not as fun as infinite Bottled Lightning.
If I were to try to fix the chirurgeon, I would give them a pretty chonky bonus to healing done with their infused
elixirs of life. I'd also add in a level 3 version, because trying to heal a 4th level dwarf fighter with 58 hp by using 1d6
elixirs doesn't sound like a good time. I'd probably also let their Perpetual Potions make Elixirs of Life – unlimited 1d6/round healing at level 7 isn't as broken as it sounds, I think. Oh, and I'd include a clarification that lets them substitute Crafting for Medicine when it comes to skill feats and unlocking higher-level versions of Treat Wounds and the like.