A historic masonic lodge in Edinburgh's New Town has become a campsite. Four men stand on stage — two performers, two volunteers pulled from the audience — practising trick shots with a baseball, busting moves and shooting the breeze. Underneath the banter, an existential crisis is bubbling.

This is Well-Balanced Dads, the Edinburgh Fringe production from Chicago's Whisper Theatre Collective, created and performed by Richie Schiraldi and Britt Anderson under the names Dick and Dale. The Guardian's reviewer, drafted on stage as a volunteer father, found himself raising his hand when the call went out for dads in the audience.

The show is part of a strand of Edinburgh comedies this Fringe season examining fatherhood from every angle — the hilarious, the melancholic and, in the Guardian's phrase, the "devastatingly accurate cringe". Alongside Well-Balanced Dads, works by Philadelphia's Lightning Rod Special and the Swedish-British comedian Olaf Falafel are probing what it means to be a dad.

Dick and Dale wear the costume of archetype. Headbands, bum bags and tank tops blazoned with "Best. Dad. Ever" — one back-printed with a power drill, the other with a barbecue. Both sport bushy moustaches, and they hand fake ones to the audience volunteers. The soundtrack is classic rock: Foghat, Kenny Loggins, Creedence Clearwater Revival. The performers take their volunteers on a road trip, casting further audience members as hitchhikers.

The set-up is broad spoof. The stakes are not. The camping-trip framing lets the show swing between goofball physical comedy and something more unsettled — the sense, as the Guardian's reviewer puts it, of an existential crisis sitting "bubbling underneath" the blokes' club rituals of ball games and dad dancing.

That tension between caricature and candour defines the current wave of fatherhood shows at the Fringe. Grief, embarrassment inflicted on children and the rituals of male bonding all find their way into a programme that treats dad-ness not as a punchline but as material worth interrogating.

For Whisper Theatre Collective, a Chicago group making the journey to Edinburgh's New Town, the masonic lodge venue adds its own layer of accidental theatre: a room built for brotherhood, now hosting four men in fake moustaches questioning what that brotherhood costs.

The fuller Guardian review, including its verdicts on Lightning Rod Special and Olaf Falafel's Helium Balloon Factory, signals that fatherhood has become one of the Fringe's live themes this season — a subject comics are choosing to take seriously, even in tank tops.