(not familiar with swashbuckler's panache - is this a feat?)
Mass suggestion, geas are spells no? it's X per day. Isn't inspiring leader is a feat (and thus class independent).
Anyway, if you think it's easy to balance an alchemist on logistics, so that its magical power is roughly equivalent to other classes, I'm all ears. Seriously, I mean it.
Panache is an at-will ability for Swashbucklers (Rogue subclass) acquired at 9th level. Aside from its combat uses, it also works as an at-will Charm ability (IIRC it's a Persuasion check contested by the target's Wisdom, possibly Wisdom (Insight)) on non-hostile creatures. It lasts for up to a minute, or more if you renew it of course.
Mass Suggestion and Geas last for weeks, months, or years, so the limiting factor is unlikely to be spell slots--you're going to be limited by available opportunities, i.e. number of potential minions. Also, you probably have to pay them to keep them on your side, so you're probably gold-limited on the maintenance side as well as the acquisition side.
Inspiring Leader is a feat, and thus a class feature which is available to any class--and so what? The point is to show that 5E doesn't really rely on X/day balance (which was done already in the Rodney Thompson quote--these other things are just illustrations for the sake of discussion). If Inspiring Leader, instead of being a feat, were an ability that Valor Bards (only) acquired at 8th level instead of an ASI, would that change the value of the precedent?
RE: "if you think it's easy to balance an alchemist on logistics, so that its magical power is roughly equivalent to other classes", my point is that in 5E, that question doesn't make sense. There is no such balance requirement. I don't think alchemy should be a class in the first place--it should be an activity--but if you did make an alchemist class I'd just say "you get to do alchemy cheaper and faster than other classes, and you learn various recipes as you advance", and then I'd throw in "you accumulate X gp in alchemical substances per month during downtime activities due to your hobbies and offscreen activities." It winds up being balanced differently than other classes (X/month freebies) but that's part of the theme of the class: you're a manufacturer. Like a wizard, your strength lies in
preparation, not improvisation.
If I made X = 100 gp/level, that would imply that you get 10 free doses of drow poison per month at 20th level. Since each dose (in my game) goes bad about six weeks after opening it, or six months in vacuum, that means you'd have a steady state of 60 free vacuum-sealed doses without spending any additional treasure. Or you could have one to three doses of synthetic purple worm venom, or nigh-unlimited quantities of regular flaming oil, or some other substance based on specific recipes you'd researched such as Potions of Invulnerability or Extra-Healing, although the latter requires other ingredients in addition to the gp supplies. (Troll mucus or vampire blood.) So again, you're being balanced on some other basis: X/vampire, not X/day.
