1. Quotation marks are not intended to convey emphasis
The beauty of typing on a computer is that you can make the font bold or italic or underlined to convey emphasis. If you are writing something by hand, you can still clearly underline or increase the size of characters you want to emphasize. You can also use the Usenet style of enclosing a word in *asterisks* or _underscores_ to convey boldness & italicization respectively when you cannot actually make text bold or italic. At least one of these methods of emphasizing text should be more acceptable to you than using quotation marks.
My guess is that this usage developed out of the use of scare quotes, quotation marks used to convey an ironic, new, or nonstandard meaning of a word. Scare quotes, by noting that there is something curious about the word, also serve to emphasize the word, just as with italics around foreign expressions or newly-defined words. However, while italic text can be used solely for emphasis, quotation marks always carry some other meaning in addition to emphasis. So using them to only convey emphasis is confusing. Please don’t.
2. Quotation marks shouldn’t stick around
This is a matter of style, so feel free to disagree, but you usually only need to put a word in quotation marks once:
(1) Martin Luther King, Jr. said “I have a dream”. His “dream” was racial harmony.
(2) My congressman has a “solution” to end poverty. That “solution” is to eliminate Welfare.
With regards to (1), you’ve already given appropriate credit for the word “dream” to MLK. You can now use it as your own. With regards to (2), we get it. Your congressman is an idiot and his proposal is a solution in his mind but not in yours. The key point here is that you can use words that are not your own, and people will figure it out all the same.
3. Quotation marks should not steal candy from babies
It’s just morally wrong.
[I apologize for the prescriptivism, but this issue has come up twice in two days and thus must be clarified. Although I suppose the fact that this issue has come up twice in two days suggests that the language is changing and I ought to get on the trolley.]