Woodlands - From a bit of Googling, I believe at one time portions of NE Richland were covered by the City of Columbia sewer system, but were transferred to Palmetto Utilities (formerly Wildewood Utilities) because of the area's belonging to the Rice Creek/Wateree watershed:
Work Session Minutes
Most of the rest of Columbia is on the Broad/Saluda/Congaree watershed, which makes utility management a bit challenging. While I would have hoped the City showed more leadership and maintain sewer service in NE Richland, at the time perhaps it made sense to them to let someone else take care of an otherwise "fringe" watershed. Now, of course, with development booming in line stretching from Blythewood to Lugoff, it may be difficult to put the genie back in the bottle.
This disconnect between watersheds, municipal boundaries, and utilites has also been a political football as Kershaw County has moved its water planning from a stand-alone relationship with the Central Midlands Council of Governments to its otherwise "home" council of Santee-Lynches (which covers other areas like Sumter, Manning, and Bishopville). This has caused concern in Richland County because now sewer and water planning in NE Richland could be decided from "outside" the region.
This is another failure of local authorities failing to think and cooperate regionally in a meaningful manner. Folks have got to get out of the comfort zones of their local commissions and boards and realize that regional growth will mean, on some level, regional coordination. I live closer to Elgin and Blythewood than I do to downtown Columbia, and that means I am pulled between the centers of gravity of differing cities, utilities, and other municipal services.
Woodlands - what you are describing is basically the Columbus, Ohio method of annexation, which is very aggressive and almost Texas-like because the state of Ohio allows it (it also has other interesting state laws like automatically designating any municipality a "City" when it reaches 5,000 people, forcing those municipalities to act somewhat responsibility in terms of municipal service - no more "Mayberry" excuses of governance). Columbus says: "ok, you want city water - fine, we get to annex you". As such, their tax base has engulfed much of the suburban and even exurban edges of the metro area. While Columbus does have its problems (they do have some declining inner-city areas), its leverage in terms of utilities and services has been a healthy stabilizing factor. Suburban/exurban residents don't seem to be up in arms over this, and one thing that keeps these annexation deals going is that suburban school district boundaries are untouched - they are still largely based on smaller township boundaries as most of the Midwest is. In fact, in the Columbus area they say it's a great deal if you can buy a house in a good suburban school district but within Columbus city limits - you get cheaper city services but quality public education - the best of both worlds. There are a few exceptions to the utility/annexation rule in Columbus (there are some suburban areas outside city limits but with city utilities - but there are negotiated agreements covering these arrangements).
I simply am not optimistic any sort of rational coordination, let alone consolidation, will happen any time soon. I feel Columbia's water system is not meaningful connected with city council governance - I don't see city leaders talking about annexation/municipal services other than cherry picking a few high-dollar tax bases. They seem interested in raiding suburban revenue sources rather than building a bigger, more cohesive city.