Many of the great aspects of this site are user generated -- these include the ability to easily find opponents and the content in the forums. Why would you want to restrict your content providers from providing you with free material by requiring that they pay for the privilege?
Quit pushing the Membership

I agree with ivanh that the premium members seem to collectively take a harsh stance against non paying members' concerns. I have no idea what that's about.
I think the exasperation and overentitlement might be the source of it, but I think it's good that everyone expresses what they find wrong without fear of being degraded.

On the brighter site I also play chess on 2 more sites and do not have what chess.com offers unless you have a full membership or a premium membership.
And what do I get?
Only to play a limited number of games, and every time I want to access anything else, the response is: sorry you are not a full time member, please take a full membership to access.
At chess.com, I personally think that too much is offered for free.
1. To play an unlimited number of games.
2. To be able to post in forums and to criticize without any foundations and any constructive suggestions.
3. To access other players games.
4. Play both online and blitz chess.
I understand the site philosophy to attract the most members and possibly convert the new members to paying members.
This should be a short term vision say 5 years or so. The next step is to make the paid membership so attractive to all members, when the site reaches 2 million members or so, that people want to join for the additional benefits.
Other than what new features or program changes what is it that I want to see? chess.com should expand on the excellent concept for chess.kids.
Possible areas of future expansion can include: qualifying to play a master for one game, personal GM coaching for a game or so, at the highest level with a personal contribution and the player assuming his travel expenses, the opportunity to play a Gm giving an exhibition, a collection of games of a given opening played by the best players over the years to see the progression of a specific opening and tactics development, the possibility here at chess.com to challenge more than one player as a team 2 against 2 players or more and possibly playing 3D chess, remember Spock Star Trek 1X, if I remember well.
You know it costs a lot to do all that, showing that Chess.com is very cost-effective.

I agree that people wanting something for nothing in this day and age is hopelessly naive. However, I have become more and more dissapointed with the memberships here. The perks of gold membership have become fewer over the years, so I am trading my yearly gold into one month's worth of diamond and then no longer paying- gold is not worth it any more...
Paul: You're saying I shouldn't be able to post because I am not paying? The forums are half the reason I come here. Making the forums an exclusive club excludes page views which excludes ad revenue. I think some of your other suggestions are ok, like paying for being able to view other players' games. Another thing I would add to the list is the meebo thing, if only because I don't use it and it's annoying.
I think the system is pretty well balanced right now. Those who care enough to use the tactics trainer etc. are the ones who care enough to pay for it. Those like me who just want to play a few games and talk with other chess people are not going to pay for this, and right now we don't have to. Its a pretty good system that has worked for other sites: chess.com gets the money from the avid players and the membership of the casual pushers.
On the original topic, I think the premium memberships are pushed a bit much (especially by premium members rather than the site itself) but it has gone down a bit and I can live with the current level of ads.