Detergent solutions do work at dissolving dirt and greasy deposits that accumulate on LP surfaces. But the problem with detergent solutions is that most people use far too much detergent. If the solutions gets sudsy, you have too much detergent.
It has to do with a property of detergents in water, called the critical micelle concentration (CMC). For many detergents (such as common liquid dish detergent), the CMC is very low, a few drops of concentrate to a gallon of water. Adding more detergent above the CMC level does not clean things better and makes rinsing off the excess detergent a problem. If you have hard water that contains various salts of limestone, it becomes a worse problem. Calcium in the lime salts forms an insoluble complex with detergents that commonly have a negative charge on them.
Washing LPs in dilute detergent solutions does work. You should rinse them afterwards, first with cold water, and then with isopropyl alcohol (1 part) diluted in 3 parts distilled or deionized water. That should remove the remaining detergent and prevent residue from building up on the LP surfaces.