I DM'd a campaign with an Alchemist in it. The subclass features are alright, but can be easily overshadowed, by group composition. The campaign went to 15th level before stopping due to work constraints from the pandemic, (Half the group are medical personnel).
Some features of the campaign worked in the Alchemist's favor, some did not.
In the Favorable Category: It was an urban campaign, (Waterdeep), with Downtime Activities enabled. Allowing an Artificer to use all of their "Adventuring Day Off" spell slots to create Experimental Elixirs for their Adventuring Day, the next day is nice.
I also modified Experimental Elixir to allow potions to be created with Artificer spells equal to the spell slot used.
In the Negative column: it was an 8 person group, 4 players were Paladins, one other player was an Arcane Domain Cleric. Spell Slot-less Lesser and Greater Restoration, and Heal while useful, were largely, unnoticed due to the PC group composition.
A component free Lesser Restoration at 9th level, lacks oomph, if 4 players could remove disease at 1st level via Lay on Hands, and the Cleric of the Arcane could remove hostile spells with Spell Breaker at 6th level. I will stress, the free spells...especially Heal and Greater Restoration are useful, but Spell Breaker steals their Thunder in a large way.
Alchemical Savant is great. The fact that it is not limited to artificer spells makes it better than an Artillerist's Arcane Firearm.
The player wanted to play something akin to a Pyromancer from Song of Fire and Ice.
Their race was Tiefling, (I allowed them to swap their ability modifiers thus +2 Int, +1 Cha), I also allowed them to swap Thaumaturgy for Green Flame Blade, because green flame and GRRM Pyromancers are thematically linked.
Sprinkle in the Flames of Phlegethos and Elemental Adept feats, and it was a potent fire spell caster, and good with Acid Splash etc.
While it took some time and effort to setup, at 1st level, the combination of the Snare spell and the Create Bonfire cantrip is Nasty! Really, Quite Nasty!
(Especially in the sewers of Waterdeep or any corridor like environment.)
In a smaller group, with less or no Paladins or Arcane Clerics, the Alchemist would have shined more.
Multiple Paladin auras and Flash of Genius, is a tremendous combination, the PC group played like it had Legendary Resistance.
My personal opinion is that Alchemist Subclass powers are not balanced for the 3rd level subclass cycle...by the level at which the Alchemist powers come online, they are somewhat diluted. Also the Alchemist should be able to make Sovereign Glue and Universal Solvent....WTF Wizards of the Coast.
Now, I will add this caveat...the Alchemist was the first Artificer I saw in play. The Artillerist's Protector Eldritch Cannon, is the single most powerful thing at lower tiers....I have not seen the Prot Cannon in play past 6th level. I suspect the Alchemist's Temp HP from Experimental Elixirs will still hold up, as you can in effect have a stockpile if the campaign routinely features Days Off.
If not, the magic sprinkler of temp HP that is the Protector Cannon is just amazing.