I think the problem with lockdowns is multi-fold.
1. They're impossible to fully enforce. When you have jobs deemed essential that aren't pure 8-5 deals, it's not like police can (or would be willing to) just start pulling people over because they're on the road at, say, 6 p.m., so if a person wants to hang out at a friend's or have a small get-together, there's probably a .0001% chance that anything would be done barring a neighbor being one of those "call the cops on 10+ people" narcs. When you take away people who aren't locked down due to having jobs where it's essential to be at the workplace, it's already not going to be a perfect success and then take away the people who have no desire to be cooped up at home all day, every day, it's just going to get worse and worse.
2. At least in Ohio, I think there would be diminishing returns on the success of a lockdown because there already was one and either due to #1 or other factors (or both), it lowered numbers for a few months, only for them to rise a lot when school started and the weather got cooler. Asking people to go through that again, along with the economic ramifications, simply to bandage the wound and provide a bridge to the hypothetical date a vaccine is available isn't going to have the same effect it did in April.
3. This is one of those things where typical vague poli-speak like "flatten the curve" and so forth really isn't going to work with people because it's something that openly effects their lives on a day-to-day basis. If DeWine had initially phrased things bluntly along the lines of "This is the plan: Lockdown for 2 weeks, this stuff will open then, this stuff will open the next week and so on. When everything is opened, we'll reevaluate our progress and determine the next course of action", while using those weeks to plan out said course, things could have worked out more smoothly. Instead, it was week after week of his lame-ass daily briefings (wife's recipes, little kids on Tik Tok, his ties, gotta fill 30+ minutes somehow; MAN, THIS IS SERIOUS!!!!!) filled with generic "we're doing good; we know this is tough; stay the course" lines that only seemed to desensitize people (at least in my general circle) from any potential threat.