People seem to be fine with using an omni-blade all day without talking about how ridiculous it is or how illogical it is in futuristic fictional setting.
The wikia about omnitool weapons:
"Although melee-combat applications for the omni-tool are almost as old as the device itself, the feature was largely unused prior to the Reaper invasion. The need to take on multiple husks in close quarters forced the Alliance to develop ways to enhance the tool's offensive capability.
The most common melee design is the "omni-blade," a disposable silicon-carbide weapon flash-forged by the tool's mini-fabricator. The transparent, nearly diamond-hard blade is created and suspended in a mass effect field safely away from the user's skin. Warning lights illuminate the field so the searing-hot blade only burns what it is intended to: the opponent.
More technically adept soldiers frequently modify their omni-tools to maximize stopping power through electrical, kinetic, or thermal energy. Some troops integrate their weapon with their kinetic barriers, transforming the omni-tool into a wrist-mounted bludgeon; others fabricate flammable gases, held in place by a mass effect field and ignited upon impact. All prove deadly surprises for opponents who expect a disarmed Alliance warrior."
If someone wants to melee you (husks, abominations and dragoons ), it might be usefull to be able to defend yourself in these close-quarters, without having to wear a shotgun to blast their behinds off. You could say the same for banshees, brutes and phantoms, but they can easily end you.