You want to give him feedback, but since your speech says you've already made up your mind, what purpose would the feedback fulfill?
I have a report who is simply no good
If his behaviors were mistakes, he could be taught and improved upon. If he is just fundamentally horrible, he can't change himself.
He's simply not a person for this job.
You've passed judgement in a way that's contingent on him being a different person. He can't be a different person.
I'd be very careful to craft a success story for this employee. If you want any kind of positive resolution out of this, you can't expect him to "not be him" and you can't expect him to harm himself (by walking out of the job without a better one in place).
Focus on the behaviors, and re-frame your mental upsets. Make his problems "problems of his behaviors / actions" and stop identifying him as evil.
Behaviors can be changed, but there's no motivation on his part to change them if, in the end, you'll just see him as bad.
often presents his - completely false - solutions to me and other people at the same time
Ok, so you have half a behavior problem here; and, half a judgement of "the solution is wrong, because it came from him" (which is a logical fallacy, if you think about it; after all, even a person who knows nothing might accidentally come up with a good solution randomly).
it's sometimes difficult for me not to express with the tone of my voice that I'm irritated
Because you are irritated, and your way of viewing this problem is likely to increase your irritation. You are not letting him fail, nor are you letting him succeed; instead, you're taking on a role you're not supposed to be performing. You're attempting to protect the company from this person because you believe they are bad; and, you're attempting to protect this person by trying to isolate them and instruct them to be someone else.
Now that I've re-framed it in a way a 3rd party might look at it, you might notice that there's no win in this for you. Since you're working on a problem without a solution, as long as you believe the problem is the person, and you are unable to keep this person in solitary confinement (one-on-one meetings when he pitches his ideas) frustration levels will continue to rise until you change a few things.
- View the behavior as the problem, not the person.
- Teach the person how to develop an idea into a plan. If the idea is truly wrong, it is wrong due to a constraint of (time, money, or manpower). By having this person better evaluate their ideas, they will contribute ideas that come with less cost (and thus more benefit).
- Listen to their plans in a way that doesn't drive confusion. For example, have them write up a description of their idea in a word document. Read the document with an open mind, and reply with non-judemental questions focusing on (time, money, or manpower).
As you stop writing off his input as "false", he'll stop seeing you as a gatekeeper which is blocking (his perceived) progress. He may achieve something, or may achieve nothing; but, right now you seem to be:
- Always right in the evaluation of his ideas.
- Always constructive (your words, not mine)
- Never offensive (despite saying a person is "just bad", which offends many)
If taken to an extreme, you probably come off to this person as "always right, and always has to control (by dragging me off to a corner to tell me how I'm always wrong)"
My point in the above was not to tell you your business, but to enable you to see that he's put you in a position of power.
You are capable of changing his views, and getting good work out of him; because, you are capable of changing your mind and your approach.
You can see him as fundamentally flawed, and guess what, you can't change that.