Note; this page is for guesses on the current comic run, unresolved matters from earlier incarnations, and guesses regarding the franchise in general. WMGs regarding the 2019 movie have their own page.
His Golden Age adventures took place in such a universe and he seldom interacted with the human Marvels.
What it does do is give him access to a different set of workarounds; basically, he puppets his bad leg around using magic superpowers as part of his disguise, and tends to hover/fly at very low altitudes in combat. The former might actually be harder than just using a crutch - maybe it wouldn't be if all things were equal, but he received extensive physical therapy with regards to one and had to figure the other out on his own.
The latter happened in 2009, the New 52 reboot in 2012. In between not much happened on the Shazam front other than one or two issues of Tiny Titans.
Sadly, the idea of him being the survivor of a right-wing terror attack is far more current than it was back in 2012.