Question about laying pavers over existing concrete

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I have a concrete sidewalk in a backyard, which was made by a do-it-yourselfer and it was a badly done job. The sidewalk looks like it was poured use=ing the adjacent grass as forms. :lol: Also, another part of the sidewalk the guy installed these ugly pink fake brick pavers, and they are desintegrating. part of the sidewalk lets two inches of water collect when the snow melts in the spring, making it hard to walk on for about two weeks. I need to replace the walk, but I was thinking- instead of demo-ing the concrete and fake brick, of laying down 3 inches of 3/4 inch gravel for drainage and for a base, and then laying some nice pavers such as flafgstone or cobblestones. Is there any reason I should go to the expense and labor of getting rid of the old concrete? The level is not an issue because the current level is lower than the house threshhold and at the other end of the walk. Thanks for your advice, Mike