I inevitably always theory-craft and daydream about character concepts for either DnD 3.5 or PF1e that I would love to play...but are just completely impractical for a standard game with other players, whether at-the-table or play-by-post.
Here are four types of games/concepts I've always wanted to play, but probably will never get the chance to:
Trapping for Fun & Profit (DnD 3.5)
Using 3.5 prestige classes such as the Trapsmith and/or Combat Trapsmith with appropriately related feats and gear to play an actual master of traps. Rather than hunting down the baddies, relying on successful trap placement, clever trap setups, and various luring techniques to win the day or at least regularly gain major advantages for combat encounters. I've yet to meet a group of players that would be enthusiastic with this type of gameplay being the focus, or even having such a concept 'bog down' gameplay. The logistics for setup and execution of such tactics, especially as a mainstay combat style, are just not practical for an at-the-table game or a play-by-post game.
Tech vs Magic (PF1e)
Taking inspiration from games like Star Ocean where a Tech-dependent hero gets stranded on a medieval fantasy world with magic, I'd love to play a Tech-based character somehow stranded in a magical world. Material like Arcforge and variant rules such as Akasha as Cybertech open up a whole world of 'technology' themed things that could be leveraged into a fun dichotomy in a fantasy world. For some reason, I don't ever seem to find many fans of the more tech-related 3pp for PF1, and certainly no one gung-ho about basing a whole campaign around such material. Hell, the entire Pilot Sphere from the Spheres of Power Wiki got retconned and scrapped by the author(s) themselves. Breaks my heart and dashes my robo-centric fantasy dreams.
Adventurer for Hire - Any Position (PF1e)
With enough 3pp (looking at you, Spheres and Akasha), anything is possible. Specifically, I've had a few theory-crafted 'Jack of All Trades' build ideas with a single concept in mind: A mercenary adventurer that hires himself out to groups to fill in whatever position they need for their current quest/job. With flexible talents (Spheres), and the ability to shuffle around Veils (Akasha) and Customization Points (Aegis - Psionics), you can literally replace just about any other character class. Which would be great...if you actually needed to. As most games have a fixed set of characters though...there just isn't ever a need to do so. It's literally a concept with limitless potential and zero practical use in a traditional game with other players. Unless all the other players bring new characters for every job, I just don't see a way of ever truly playing a Jack-of-all-Trades character concept that would actually be able to live up to their true potential.
Damnit Jim, I'm a Doctor! (PF1e)
Medic. No spells, no cleric, no convenient potions to heal every booboo, etc. Just a strung-out Medic character who has to try to keep his party alive via pseudo-conventional medicine. The Medic class paired with feats like Field Medic (3pp) and Asclepian Doctor (3pp) to actually use the Heal skill as an actual replacement for cure spells instead of stop-gap measures, and eventually using feats like minor-medical-miracle to resurrect the recently dead in place of resurrection magic. The only way to make the concept viable though, is if everyone is generally magicless and staples of the game like potions are not available just to make the healer's character concept viable.
Games I'll likely never experience, but one can always dream.