The City put some effort into cleaning up Prospect in the eighties, and all the hookers moved to Detroit and Lorain around then. Not sure why, though.
Street prostitution exists where there are drug houses and street dealers. Those side streets off Lorain, and the side streets throughout the near west side, have many drug houses. The street hookers are on all-out, around the clock binges on crack, smack, or whatever. 100% of them. If someone wanted to be a prostitute and wasn't an all-out drug addict they obviously would be escorts instead. And these all-out drug addicts never want to be far from the dopeboys they buy from, the drug houses they crash in, and the other drug addicts they are bingeing with. They are doing drugs 24 hours a day and constantly need to be able to get quick cash and quick fixes. Once a neighborhood is established as a place where drug houses can be set up and people can get quick cash and quick fixes to support doing drugs around the clock, it's very hard to root that out. (As for Euclid and Green, add to the drug houses the fact that there are multiple cheap motels for hookers to work out of.)
There are other factors that make Lorain Ave. a prostitution area. It is somewhat safer than the east side prostitution areas (not TOO safe, though -- a prostitute was shot at West 73rd and Lorain a few weeks ago...although she's right back out there now). It's a poor neighborhood but it has a steady flow of Johns with cash passing through. Some of the businesses in the area sell drug paraphernalia. I don't want to name business names here because I don't want to be accused of defaming anyone, but there are certain gas stations in the area that sell, for example, "kits". A drug addict will ask for a kit and from behind the counter they are handed a paper bag containing a glass tube (for a pipe), a lighter, and Chore Boy (used as a filter for crack pipes). When they need clothes on the cheap, they walk to the big thrift store. They have everything they need in that neighborhood to survive without thinking about anything else but drugs and getting money for drugs (that's why they are drawn to the lifestyle when running away from the problems in their lives). The whole neighborhood is well suited for a drug addict to binge in, and because it's gone on so long it has become tolerated to an extent (by the police and the residents).