How useful is Undermount Kitchen Sink?

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As others have pointed out - the main advantage is the ability to easily push water and food particles from around the sink into it without having a lip.

Over time, a sink that is installed from the top will almost always begin to leak as the gasket starts to wear out - resulting in water under your sink.

They are exactly as useful as any other type of sink, except that they are easier to clean around. That's the ONLY difference, aside from the price. 

They are FANTASTIC!  I love them because you can just push stuff (crumbs, etc.) into the sink without worrying about a sink edge sticking up.

I prefer because you can just sweep or wipe counter things directly into the sink without the lip

Theres no advantage or disadvantage.  Its basically for looks. It gives a nicer finish when your installing a stone counter top.

I've got one now with recently added granite.  I'm not a big fan b/c splashed around the edges are a pain the butt--constantly need wiping up.  One thing ( or 2) that I'm adamant about is get the deepest sink you can find and I would NOT OWN a single bowl kitchen sink.  I hand wash a lot of stuff, (pots and pans, cookie sheets, air fryer buckets...    I use two sinks 2 or three times a day.

As useful as any other kind of kitchen sink that holds water and has a drain.

depends on what you want personly i don't like them because the underside of the bench over hang gets dirty 

Rather depends on the material that it is undermounted to, fine if it is under slate or resin, more problematic if if is timber, unless it is something like teak.