Dropping a cowl, busting/stripping a fastener, damaging baffles and tearing seals can result even if you are careful. Of course all MX are perfect and never to any of these things... but the OTHER shop must have. lol The amount of tools I have found in engine bays and cowls is ridiculous. Even one is to many (and right now I've found almost a dozen). ALso some AC have left/right hinged cowls that make your point moot... but hey, YOU'RE THE (in your mind) EXPERT lol.
Ignoring people trying to act like the smartest in the room even if you took off ONLY the top cowl you could do the other tasks.
The evac method is cleaner (no spilled oil on nose wheels/struts/airframe) and faster (again, not having to take of ALL the cowls in most situations). Way less fasteners are involved, and less moving stuff around means less stuff to get damaged.