I've noticed that a lot of people who use 'drawer' don't have English as their primary language. This makes it more understandable, since there's no GOOD reason a 'drawer' isn't 'a person who draws'. A painter paints, after all, and for some reason you can be an 'artist' but not an 'arter'. But obviously to anyone who grew up speaking English and isn't 10 years old, 'drawer' is just a terrible word when not relating to furniture.
Using 'times' as a verb (i.e. 'to times') is perfectly acceptable informally; it seems more like it's becoming the latest "irregardless", where it is actually a word that exists and is commonly used in given contexts but is seen chiefly as being used only by those who are illiterate or otherwise lacking in their understanding of English.
Similarly, the use of 'drawer' to mean 'one who draws' is also perfectly acceptable, but, like the above example, is used little, and so is often seen as incorrect.
The difference between times, irregardless and drawer is that both times and irregardless 'work', for lack of a better word.
Drawer, however, is unwieldy upon the tongue. Grammar/spelling/etc is a vehicle of meaning and ease. Times and irregardless fit within that. Drawer, doesn't.
On a slightly related note, I hate when people to correct 'I could care less', to look educated. The thing is, 'I could care less' is a shortened phrase. Originally, the saying was sarcastic. 'I could care less, but I don't see how!' Because it was a popular phrase, it was shorted to 'I could care less'.
The OP didn't criticise 'drawer' being unwieldy, he criticised its use as meaning 'one who draws' (I assume; I doubt many people use 'drawer' to mean 'artist' and use it more to mean 'one who draws'). That it's not spoken very easily doesn't invalidate the fact that it's correct when used as meaning 'one who draws'.
I'd argue that 'obfuscate' doesn't exactly roll off the tongue, but does that mean it's not correct to use?