/---/ Having lived in NY for 45 years I can tell you they have a serious situation. The sewers date back to the early 1900s. It is so bad they outlaw garbage disposals because the system can't handle the volume. In fact, they still have wooden water pipes under the streets that date back to the late 1800s. BTW a fatberg is a congealed lump in a sewer system formed by the combination of non-biodegradable solid matter such as wet wipes with grease or cooking fat. They have become an increasing problem in recent years, with the combination of aging Victorian drains and the rise of disposable cloths.
This is actually a valid issue. The main cause, as you said are those sturdy wipes people started using. They also have a habit of clinging to the bar screens in plants, and the ones that get through have a propensity to wrap around rotating assemblies, like pump shafts and impellers.
The problem with using garbage disposals is one of sheer load to the facilities. Using them would increase the amount of sludge that needs to be digested, which would require expansion of digester capacity, which is difficult because most of the plants are severely land limited.
The powers that be would actually love to allow garbage disposal, as it would increase digester gas production, and digester gas in considered s semi-renewable resource (it's carbon, but short cycle carbon). This would allow the plants to either run a lot more themselves without added energy inputs, or if run effectively enough, provide at times additional power to the grid.
Most of the sewer infrastructure isn't as old as the water pipes, as taking sections of sewer out for upgrade is easier than taking out sections of water pipe.
The sewers are usually shallower and easier to reach as well.