"Without it I'd get sloppy"
This is the fear that keeps most people polishing long after they've seen what it costs. If I stop checking everything five times, mistakes will get through. I'll turn into one of those people whose work is full of errors and who doesn't seem to mind. The dread is unpleasant, but it's my quality control, and without it there'd be none.
I take this seriously, because it contains a real question. What does keep your work good, if fear doesn't?
Part of the answer came in chapter 3. Your standards keep it good. They're a separate thing from the dread, and they don't leave when the dread is turned down. You'll still know what a clear sentence looks like. A wrong figure will still bother you, as it should. The skill and the taste that produced the Sunday version in two hours are yours, and they don't depend on being frightened. Remember what Hill and Curran found when they separated the two dimensions. High standards with the worry removed went with the least burnout of all. Stoeber and Otto's review found the same group doing well on most measures. If the fear were what powered the quality, you'd expect people with high standards and low fear to do worse than the frightened ones. They don't.
The second part of the answer is that fear is a poor inspector. The proofreading study in chapter 4 showed it. The students with perfectionistic standards caught no more real errors, and they raised more false alarms. An anxious checker rereads the same paragraph four times without taking it in. They fix things that weren't broken and sometimes break them. They're often too tired to see what's in front of them, because they were up until midnight the night before doing the same thing.
It's useful to look at how accuracy is achieved in jobs where it truly matters, and this is general knowledge and not something I've researched for this book. Airlines, operating theatres and accounts departments don't rely on individuals feeling dread. They rely on procedure. Pilots run a written checklist. A second pharmacist checks the dose, and a colleague who didn't write the figures reviews them. The check is specific and it has an end. It's also done once, and often by fresh eyes. When the checklist is complete, the plane takes off. Nobody goes through the checklist six times, or lies awake wondering whether to go through it again.
That's the model I'll suggest in the next two chapters. It swaps a vague, repeated, frightened search for a short, specific check that you carry out once. A check like that catches more than the search did, since a list tells you what to look for and a worried mood can only tell you to keep looking.
There's also the matter of which work deserves your full care. At the moment everything gets it, which means that in practice nothing does. The supplier summary and the note to the window cleaner draw on the same limited store of attention. If you spent less on the many jobs that need a five, you'd have more for the few that need a nine. Your best work might get better. It's a common experience among people who loosen this habit, though I can't promise it and I've no study to cite.
Then there's the blunt version of the fear, which is that you'll make a mistake and it'll get through. Yes, you will. You make them now. Every document you've ever sent that was longer than a page probably had something wrong with it, and you've survived all of them, mostly without knowing. Nobody chooses between a life with errors and one without. Everyone has some, and the choice is whether you spend your evenings trying to prevent the last few small ones as well.
When a real mistake does get out, the response that works is dull. You correct it, tell whoever needs to know, and carry on. "I've spotted an error in the table on page two, corrected version attached, apologies." A correction like that, sent promptly, does more for your reputation than the mistake did against it. People trust someone who owns up to a mistake promptly a good deal more than someone who seems never to have made one.
So the honest answer to "won't I get sloppy" is that you'll make slightly more small errors and no more large ones. The large ones are caught by the single proper check, and the small ones don't matter to anyone else. In exchange you get your evenings back, and your work arrives when it's useful.