I wouldn't say "sloppy." It is not a good habit to attribute misunderstanding and possibly bad teaching to ecclesiastical virtues (sloth, pride, envy, and others). The ages of these bad spellers or their backgrounds may actually come into play. A lot of the people on-line are what you would call "kids." Many kids do not have the whole Chicago Manual of Usage memorized like we writers do, eh?

It just looks like these people are spelling based on what they hear. In the English language, there are a few floating sounds which are based upon the configuration of groups of letters and not letters that are actually seen in the alphabet. Among these letters are the "Y-glides" and the "schwas."
The 've (have contracted) sounds a lot like of if you consider the schwa (signified by an upside down e in pronunciation).
Before a consonant sound, the contraction is pronounced as a schwa sound: /ə/.
The word "banana" is a good example of the schwa. Banana is pronounced bun/ nah/ nu. The u's are actually schwa's: bə/nan/ə. Someone who does not know this, may spell banana, "bunanuh," because that is what it sounds like.
So, I imagine, the people you are talking about are spelling would/əv. (Do you see that U sound schwa?) But because they are not checking their work, or do not care, they are writing would of. Even would've has that schwa sound in the contraction. You do not say would-vee, it is would/əv. So it is a spelling error, nothing more.

This makes English hard to learn for various people who may speak another language at home. I came to this country and began to learn English only 3 years from the time I started school, so most of the internalized rules had to be learned "on the fly" since I looked like I should know all that English stuff. I learned a language with no invisible secret letters in it. I used to have a heck of a time remembering how to spell "sugar." Where the heck is the SH sound in sugar? Or sure? SH is not in either because it is another of those invisible letters. (Trivia: Where else is the S sound pronounced as SH? Irish Gaelic!)

Historical vowel shifts, dipthongs, and the borrowed use of at least 5 (main) languages make English one of the hardest languages to learn for some people.

Hope this makes sense.