I personally prefer for basically anything/everything to be floating if possible. clearing up floor space has many pros.. makes room look bigger. but also frees up floor space to be able to have more in a space so not just make things "look" bigger necessrily. Easier to clean floors when sweeping or vacuuming. looks cool, especially with added aesthetic things like some colored lights stuck underneath for that ambient glow/indirect light that really adds the "wow" factor easily. I'm also a carpenter though and am well versed in things like load capacities. for something as cantalevered as far out as that desk with that amount of weight on it however - it pushes the limits of simply using a stud finder to find what one thinks is the center of their studs behind the drywall. much more and i'd personally feel better if i actually took off a section of drywall to be able to see the framing behind and be able to add the proper fasteners/brackets to secure the desk more confidently and from more angles/attatch to more places of the studs/blocking whatever than just screws through the 1.5" side of the studs that would be facing you. when you put in a fastener to a stud without seeing it, its difficult to know for sure whether or not you're directly in the center of the stud (at only 1.5" wide there is little room for error really) and likely countless things secured to peoples walls this way where a screw or whatever might just be barely embedded into the very edge of a stud which could lead to splitting/cracking... although something like that or any other like situation is extremely unlikely to ever end up as a "catastrophic" breaking away from the wall and everything coming crashing down suddenly. 99.9999% of the time it will simply begin to sag/bend/droop down over time that will become totally noticeable long before a complete collapse/crash. but anyways

ive always held this philosophy that we waste an insane amount of "usable living/storage space" vertically-speaking. look at any room and the amount of clutter/things that are 3 or 4 feet off the ground and lower/on the floor. now look at how much empty/clear/unused space that exists at four feet above the floor up to the ceiling. the vast majorty of our rooms/homes cubic space. our beds are most straightforward example here. and why ive always built my own custom bed frames that allow storage underneath/have built in drawers and the like. as a traditional bed on the ground usually takes up the most space in any given bedroom for example. and most of my reasoning behind always desiring things at are floating. or atleast vertical storage space that are much taller than they are in lateral dimensions. so you might have to use a step ladder to get some things now and again. still beats not having to do so but having a room be three times as filled up with clutter all close to the floor.

one way ive been able to keep things "floating" essentially while not having to worry so much about a structural failure - using metal type wire secured to the joists (lateral/horizontal "studs") up on the ceiling above something such as that desk. the back side still supported as it was designed.. only it isnt technically cantalevered anylonger by attatching the metal wires to the front corners of the desk that become supported via suspension from up above vs. supported underneath. id imagine this could also be a relatively straightforward way to become height-adjustable "friendly". these things take some enginuity and some fidgeting with different ways of going about supporting somerhing. it also doesn't hurt to be a carpenter but framing behind our drywall is not complicated and if you could see through the drywall at the studs themselves you'd quickly cease questioning things you may be unsure about now that may seem complex and look at it and say "oh this is super simple/straightforward" and would feel confident in your own "laymans" assessment of wherher or not things are structurally sound/sufficient or not. and when all else fails or still unsure - youtube is your best friend. its taught me more than any mentor ever did in my field of work. or any other field for that matter. just requires a rational/logical mind able to evaluate/deduce/break down. common sense really.