You're wrong about this. Not all debt is purchased by collection agencies. Most of the time, the original creditor attempts to collect the bad debt for 6 months. If they can't collect it, they outsource it to a collection agency who gets a commission on what they collect.
You're a bit confused on this point. Yes, the debt gets "charged off". However, the moment the original creditor gets any payment on it ---whether from the debtor or a collection agency, that is considered income so the original creditor is not double-dipping as you're implying.
As far as debt being purchased for .01 - .05 on the $1.... that is typically debt that is so old and deemed "uncollectable". Any "fresh" debt (such as the OP) would not be sold for "pennies on the dollar".
As far as dealing with the original creditor rather than the collection agency? You're wrong again. Once a company puts the debt into collections, they're pretty much washed their hands of it and don't want to deal with you anymore. Sure, you can send a payment to the original creditor but that will only prolong your delinquent status because until your payment clears and the collection agency is notified/given their commission (yes they still get commission if you pay the original creditor), you are still considered to be in collections.
But that's the thing, there are a lot of different senarios the OP (or any deliquent debtor) could be looking at. It could be the orginal creditor still ownes the debt and you're dealing with in house collections. It could be the original creditor outsourced it to an outside debt collector. It could be that the original creditor sold the debt for less than owed to a debt buyer (at a slight discount or pennies on the dollar, or anywhere in between), and it could be that it's been bought and sold serveral times by various debt buyers. And sometimes debt buyers turn around and hire outside collection agencies! Every situation is unique, and any debtor should do as much research as possible to figure out who they are dealing with. Once you know what the score is, you can make better choices on how to handle it. What works with an original creditor may not work with a collection agency, and what works with a collection agency may not work with a debt buyer.
And some original creditors will pull an account from a collection agency. They may or may not, they certainly don't have to. But if a person comes across as willing to work with them (either a payment plan or an offer to settle in a lump sum) it has been known to happen. You don't know until you ask, the worst they can say is "no" after all.
Pay-for-deletes (meaning you pay the debt and the creditor agrees to either take the whole thing off your credt report, or they report it as a positive account) aren't that common, but again they have been known to happen. Usually you have to offer to pay in full with little or no negotiating the amount down at all. If a person can afford to settle in full, it's worth a shot to ask, again the worst thing they can do is say "no".
And yes, if you negotiate for a lower amount, the creditor will probably issue you a 1099 and you'll have to claim the forgiven amount on your taxes as income. But it's still less expensive than paying the debt in full.
Now, while paying what you owe is always a good thing as far as karma is concerned (plus it helps you to avoid lawsuits), it probably won't help the OP's credit report much, because unfortunatly a paid collection is almost as bad as an unpaid one. The good news is that as that negative mark on your report ages, it counts less and less towards your score, and will eventually (after about 7 years) fall off your report. It won't haunt you forever!