I think a side view game sounds pretty fun. It’s such a classic video game / platformer style that just seems well suited for adventuring.
I wonder about depth (moving in 3d around obstacles and monsters). In a Mario game it’s kinda built in that its 2d and you jump over or on stuff, but what about a more standard fantasy game? how do you handling the 3d aspect of the environment? …do you just say nah, and keep it 2d
In the Mario Bros games I ran it was straight 2D throughout. I think it worked so well for that because the maps I made were cut from Super Mario Bros, Contra, Mega-Man, and Metroid. It had that 2D knowledge kinda baked in. It was gonzo fun.
I have definitely used a side view “dungeon” or encounter in a VTT or at the table. Some examples that come to mind are: fight your way up or down the icy/windy cliff face; navigate in zero G through the levels of a starship; parkour your way across the giant chasm; or make your way up the chutes and ladders to the Donkey Kong boss.
I think these sorts of encounters add a ton of fun and variety to a campaign. That being said, I personally would not run a whole campaign this way. I think you lose a lot of the details and contextual clues that normal top-down or isometric maps provide. As @NightWorm points out, players intrinsically want to know where cover and concealment are located on the “map,” and it’s just a bit harder to answer those questions in a side scroller.
That being said, your drawing would be super informative in terms of a vertical dungeon for a DM. I would use it as a guide for how the top-down maps connect. Anyway, just my two cents.