The City of Pittsburgh KS is built on top of deep underground coal mines that kriss kross the city. Sometimes you can hear thunder rumbling through those underground, mostly water filled tunnels long before a cloud is visible on the horizon. I often wondered how long it would be before that all collapsed swallowing up most of the city? Nobody seemed very worried about that though.
I read a book some years ago called Dallas Down. A pretty good yarn. The plot was that we have been pumping so much water out of the aquifers that geological tests showed that a vast cavern had developed below the surface and it was a relatively short period of time before that cavern would cave in creating a sink hole that would swallow up most of the City of Dallas. They solved the problem by re-routing the Rio Grande and running the water into the cavern and filling it back up.
I asked a geologist friend how plausible the scenario was. He said enormous sink holes were quite plausible and not all that uncommon. So sure one could develop within a large city. He didn't think rerouting the Rio Grande to fill up an aquifer was too plausible though.
Aquifers are rock formations made up of a porous material. Sandstone is a very common
aquifer material as it is very porous. The problem with aquifer depletion is that they do indeed collapse. Phoenix AZ is about three feet lower than when it was founded due to aquifer depletion. Rerouting a river will not recharge an aquifer, once the aquifer is depleted to a certain point it collapses and can no longer be recharged because it has now lost its porosity. Also sinkholes can form but they would be very small and completely unlike the sinkholes seen in karst topography. Richmond CA recently had a sinkhole form and that would be the type you would see in Dallas (provided there is not a deeper very thick, over 300 feet thick, limestone layer that would indeed generate a karst type sinkhole)
but nothing else would happen.
One other thing to consider is that water pulled up from an aquifer is called "fossil water" because it takes around 1000 years for water to flow through an aquifer, that is the reason why you can't recharge an aquifer with a river, the water simply runs over the formation with very little being absorbed.
Yet another example of how the world operates on a much longer time frame than we humans.