If I understand correctly, what you're proposing sounds similar to what an Opera employee (can't remember who) proposed in one of those "Five things I like to see in Opera" meme that went around a while ago (it should be noted that many of the things proposed there ended up in the browser, so it's not that Opera Software does not listen) that Opera should add a robust extension system, cut off some fat from the browser, and let those removed features live a second life as an extension, essentially offloading development costs to the community, which would continue to maintain and develop (important) the feature, while Opera Software focus in the browser core.
One of the things that you mention ("hiding" features) is probably being considered at Opera, or even implemented. It's a given that Opera 10 will have a redesigned GUI, and not just a simply new theme, so probably part of it will involve increasing the usability shifting menus around, and making a new "Preferences" screen (or so I hope).
I said it other times that we have discussed Opera in DC (which must be the most discussed non-DC app around here :D): Opera Software should fix some of its ways, but in order. First, and above all, is to fix Opera 9.5, which while is still a great release, it has many broken things that make it appear less good than what it is. Second, it's to fix many of the old issues that have been reported to the bugtracker years ago, and still persist in the browser (and arise from time to time in the Opera forums or the Desktop Team blog). With all of that fixed, they should focus into what I perceive are the most pressing issues judging from would-be Opera users: lack of extensions and marketing.
As you, I definitely think Opera needs a huge push to market the browser much better than what it's doing now. The primary problem in Opera perception to the public is that most ignore the browser as a whole, for various reasons. Even when the media focus on it, you can tell a veil of ignorance (not the right word, but I can't come up with another right now) in the reports, as it's the first time they ever touched the browser. As an example, the link that fenix posts above about the EU investigating MS for bundling IE with Windows (that would be material for another thread) was reported in the newspaper I usually read as a posible benefit for the competition of IE, like Firefox and Google Chrome. Nothing was said about Opera or Opera Software, despite filing the complaint (then again, the quality of reporting in this particular newspaper has been going downhill for a while).
The problem is how to do it right, and if they're willing to do it. Doing it the Firefox-way it's not really a nice option, because at its heyday it acquired a religion-like pushing, and in certain of its current initiatives still feels like that, and you risk alienating many would-be users, and although it ended up working in the long run, it would be preferable to do it in a nicer way (I ignore how, I'm not a marketeer :P). But Opera Software, despite taking some steps towards this in recent years, it still does not seem ready to do the big-push.
Also, I would like to do some remarks over some of your opinions there: Chrome does not really have a bigger marketshare than Opera yet, it may seem like that because of Net Applications numbers, but those are U.S. based AFAIK, and not really trustable. xiti, for example, which measures browsers market share in Europe, gives a whole different set of numbers. Besides, Google quotes a installed user base of 10 million and Opera around 30 million. Also, Chrome relies on the Google brand first, and its technical merits and lightweight design second.
Probably Google also played a part in when to drop the ads in the browser. Opera Sync is far more capable than Foxmarks, although the initial feature set was similar. And Widgets are not extensions by a LONG shot, perhaps they were inspired by them, but at best they're a poor imitation. To this day I still can't find what's the reason behind their existence, perhaps the Widget specification they submitted to the W3C will make them more powerful with time and thus more interesting, but so far I don't really care about them existing or not.