What…is your reasoning for this assertion? An 8th level wizard has 12 spells slots per day before even factoring in Arcane Recovery, so that’s between 1.5-2 spells per encounter, assuming the usual 6-8 encounters spiel. Spells are not something you really have to hoard as a caster class in 5e, much less wizards.
How many of them are really going to matter enough to turn the tide of the battle?
One slot will be mage armor. Probably at least 2-3 for shield. Really he has the tools to show off a few times per day.
And an action surging GWM fighter can show off just as many times per long rest, smacking down half a dozen mooks or one big tough critter in a single round.
Im not sold on the 'Fighters cant contribute in non combat' either. Fighters are just as capable of roleplaying as anyone else, and have access to the same social skills as a Wizard does. They dont get charm person, but they do get more feats (so more things like Actor and the like if they wanted to be socially inclined).
I could use my 2 extra feats as a fighter for Skilled (persuasion, deception and insight) to go along with intimidate I get as a fighter, plus take Actor (or persuasive, empathetic etc) as a feat on top. With an appropriate background Im solid as a party face.
Just using fighter class features.
Remember 99 percent of social pillar encounters are resolved via roleplaying (with a social DC usually at the end of it, based on the outcome of that roleplaying). Wizards might be able to charm person their way through the encounter, but the charmed creature knows this afterwards, and this comes with complications of its own.
And charm person only grants you advantage to the social checks. A wizard is still better charming a critter, and then sitting back and letting the (rogue/ bard) doing the heavy lifting.
Same deal with environmental challenges. Most of can be dealt with via a rope and a 10' pole. Athletics also helps with swimming and climbing. If you cant teleport to the dungeon, who cares? If the DM has set the encounter in a dungeon 1000 miles away he's going to provide you with the means to get there via macguffin, or it gets resolved in a montage anyway (after weeks of travel, you arrive at the dungeon entrance..).
If you have a party of fighters and the DM sets the adventure in the 5th plane of Hell,
he'll be providing you with the means to get there (a magic gate, an NPC, artifact or other means of getting there via macguffin). Sometimes the macguffin will be a fellow PC (the wizard) who gets to cast plane shift and feel all chuffed about his awesome power (when all he has done is avoid the DM doing it for the party instead).
99 percent of the game is killing stuff and taking their things. Its where the advancement (XP) of the game lies, and its why the third book of the three CRB is dedicated to monsters (and not to social encounters or environmental puzzles). All abilities are framed in combat jargon (on your round you can do X as an action etc).