Absolutely.
1. Finding equipment of level is like .0000000001% chance (maybe a slight exageration, but not a huge one. If 100,000 items drop and one is level appropriate, I would be surprised.) Add to that the fact that just being level appropriate isn't enough. You can still get level appropriate junk.
How does this push you to the auction house? 'Level appropriate' means nothing. Its just words you are throwing in there to make drops seem rarer than they are. An item is either useful or it isn't, there is no detriment to using a lower level item other than its stats potentially being lower than other items. My level 60 Barbarian who is in A3 Inferno is still using level 53 and level 56 rings. The bottom line is that if the drop rate of items is tweaked to the point where you can continue to advance just through your own drops, thats exactly where it should be. I leveled my first character all the way to 60 without touching the AH, I know many others who did as well
2. Selling items in game to the vendors yields next to nothing in the way of monetary loot. If you want to make any cash what so ever, you are strongly incentivised to go auction house.
Vendor items cost sub-10k all the way up to Inferno. What exactly do you need gold for if you aren't planning on buying things from the AH? Are you really saying that Blizzard is pushing people to use the AH by making people need to SELL on the auction house before they can BUY on the auction house? Do you not see the ridiculousness of this statement? AH is not needed for progression, you do not need to sell on the AH if you dont want to buy on the AH, therefore nobody who doesn't want to use the AH already is being incentivized to use the AH.
3. Items SELL from the vendors at something like 500X what they buy from you for. Quite a markup, but it keeps the players in constant need of cash. And then why sell for peanuts, if you can sell for reasonable rates in the Auction house?
Once again, the only people who need care about the amount of gold they get from their loot are the people who want to buy from the AH. They already made the decision to use the AH on their own, the fact that they can get more from the AH for their items is not some kind of evil money grabbing scheme designed by Blizzard, its simply a side effect of having an in game economy.
4. The Blacksmith and the gem dealer require cash to upgrade in order to give you better stuff as you progress. And your Stash is also severely restricted unless you buy it larger. So cash is a premium, yet selling loot and even drops of cash are severely limited. So why not go to the auction house?
What were you expecting? Someone who can craft you the best gear in the game for no cost? I can't see how this is linked to the auction house - this is an EXPECTED design decision, auction house or not. Its a crafting system (or gambling system might be more accurate in the case of the Blacksmith), it would be crazy if it didn't cost gold. Getting the gold to afford upgrades is not that hard. It does require you to sit down and farm a bit if you constantly want both your Blacksmith and Jeweler to be on your level, but they are not required to progress, and Blizzard has already acknowledged that the upgrade and crafting costs are too high and they will be adjusting them down. I don't see any kind of correlation to the auction house here. The auction house is there, it is available, it is not mandatory. You could just use a bot to get the gold, because by your logic, if its available then Blizzard must be pushing you towards it right?
5. Then there is the auction house. You can now 'Buy' level appropriate stuff from other players. You can now sell stuff that the vendor won't give you 10 gold for, for thousands of gold. And you can pick and choose from appropriate items instead of whatever randomly drops.
I don't understand what your point is. There is an auction house available to buy stuff from, it is not needed for you to progress or enjoy the game, Blizzard has not made any design decisions to force you to use it. Once again you seem to be arguing that the existence of the auction house is in itself an attempt by Blizzard to push people to use it.
Don't get me wrong, you can navigate all of the above without ever once using the auction house. I know because I do. I won't get sucked in to the Auction house. But it is 100x easier to use the auction house. The idea is the same as crack dealers use. Give them a taste for free, and make the alternative harde. Pretty soon they are hooked. Why farm for good stuff when you can buy it. Don't have the gold? Go to the Real money auction house.
And here you admit that you already know the auction house isn't required to progress and enjoy the game. You haven't mentioned a single mechanic that is designed to make people require the use of it, but you still want to see it as being shoved down everyones throats. You see what you want to see.