The lagoons (the proper term) are artificial constructs. They are not natural ponds that were converted into waste holding sites. They are designed by engineers and constructed specifically for the purpose of storing waste. The EPA has rules governing their construction, one of which being that they must be large enough to contain all of the waste generated by the farm for 12-18 months, and have sufficient extra storage capacity to be able to stand up to a 100-year storm event. Essentially they have to be big enough to hold all the waste, plus all of the extra water from the largest rainfall event the farm is likely to experience this century.
Now, these lagoons can occasionally leak, but that is why they need to be inspected periodically. Engineers come out and look over the walls of the lagoon, take samples from local surface and well water, and if there is a problem with the lagoon they require it be fixed or replaced.
Under normal operations a lagoon is filled over the course of the year (running generally from late spring to the end of winter) and then the contents of the lagoon are spread on fields as fertilizer. The lagoons are rarely drained completely, but they reach an equilibrium where the amount remaining in the lagoon each year after the farm is done fertilizing is roughly the same from year to year. The lagoons act not only as a reservior for the manure, but as a digester as you indicated. They break down much of the wasted feed (pigs are pigs after all) or previously undigested organic matter in the feces. This acts to do 2 things. First it increases the availability of nutrients in the manure, making it a better fertilizer. Second, it results in a reduction in the total amount of waste. Methane, H2SO4, and various other gasses are produced by the microbes in the lagoon as part of the digestion process. There have been various attempts to capitalize on the Methane production specifically, and a lot of work has been done on trying to reduce the production of noxious odors like H2SO4. I have even seen farms which utilize equipment to separate the solid parts of the waste from the liquid. The solid is then composted and sold as garden fertilizer, and the left over liquid is then used as both fertilizer and irrigation. However, it is feces after all and there is no reason to expect it to smell like roses.
As to the "economic damage", I would disagree. The on farm jobs, and down stream jobs that animal production creates (truck drivers, slaughterhouse employees, grocery stores, local butcher blocks, meat inspectors, etc.) are a net positive for the economy. These lagoons do not routinely leak, and anyone making claims to the contrary have a political axe to grind in my experience (PETA, ELF, ALF, etc.). Hell, you even indicate where some progressive farmers are using the methane to create extra profit for themselves by selling back surplus electricity to the grid (which the electric companies in some areas are not actually pleased about according to a dairy farmer I met from California).
Basically your view contains all real components of animal manure handling, but is based on an mistaken impression as to the prevalence of leaks, which happen rarely and a very big deal when they happen (as opposed to being glossed over) and the true purpose of a lagoon. The lagoons exist to improve the fertilizer value of manure, and hold it so that it can be spread at the best time of the year for cropping (spring around planting time). I worked on a very small dairy in MA that did not have a lagoon. They utilized straw and a recessed lane in the floor with a chain that dragged the dirty straw and manure out to a pile. They were forced to spread manure every couple of months in the summer because they didn't have enough storage space to go all winter. They were a small operation as I said (~30 milking cows at a time) so much of the regulations don't apply to them, and fortunately they didn't have any surface water close to their farm (no streams, brooks, lakes, or roadside drainage). Their frequent land application in the summer probably resulted in them seeing reduced value of the manure because much of the nutrients in the manure had not been digested sufficiently for crops to be able to optimally utilize them that year. There is also the fossil fuel used to repeatedly drive the tractor & manure spreader further and further from the barn in order to find unfertilized land (which makes the bulk reduction properties of a lagoon all that much more valuable).
Lagoons are required for farms that produce large numbers of animals in an intensive husbandry situation. They are heavily regulated and there exists extensive legislation governing their construction, maintenance, drainage, and decommissioning. Accidents do happen, but planes also fall from the sky and cars crash on occasion, through means devoid of malice or negligence. Hell, the Purdue University Swine lagoon is less than 100 yards from a natural pond with cranes, geese, ducks, various fish and amphibian species. If that lagoon were to leak, that pond would die almost overnight, and during the 8 years I was there it never happened.