C'mon, even the PSP has little trouble displaying most pages and that little thing has 32mb ... I'm using old PCs with cpus clocking in the hundreds and only 256mb, and there isn't a page that they have trouble with. The only kind of modern day stuff it can't keep up with is decoding HD movies of games (apart from playing games of course)
But much more importantly, the Cell architecture is way more suited for showing webpages than traditional computers are. It's one of the core features the Cell was designed for. Rendering and downloading a page is something that can best be done in a number of different threads. Heck, Cells will be used for heavy weight servers, never mind a few clients. It's all about streaming data from multiple channels. The Cell was built to work together with other Cells over networks including the internet from it's very core.
If anything is going to stop the PS3 from beating the PC, it's not going to be web-browsing. Browsing the web has become one of the most platform independent things out there, with two of the three main webbrowsers available on other platforms.
In the end what is really stopping people from getting other machines, is because the corporate world works primarily with them.
Ironically, I've encountered several people who were afraid to browse with their PCs, because they feared they'd infect their computers with Adware or virusses. One of them bought a Mac. I hate him for it, because our IT department (of which I am a part, though as a programmer, I suffer slightly less) will not have a good time giving him any support.
I don't consider this a trend necessarily, but it does indicate you never know. Maybe messenger will be the primary reason for people to keep their PC for their online stuff.
We'll just have to wait and see. Personally, I browse so much, that I can find use for just about every browsing device in my neighbourhood. So if the PS3 can do it, great. It has a 1Gbit Ethernet connection, so that should last a while, and it should do sites with lots of video like gametrailers and gamespot rather well, I imagine. What I am really hoping for is that I can have a browser like the PSP's as well as a full Opera or Firefox browser (either through Linux PS3 or something else). Because the PSP's browser is very good at accurately displaying the page and is at the same time very resistent against adware or virusses. Just a while ago I went to a Japanese site, and downloaded a game demo straight to my memorycard, and could then play it from there. You can also save all sorts of other media - no special portals are required for this.
Families will have lots of people browsing, so another browsing device not only won't hurt, but will actually be quite likely to be used. I even see a future for the Opera browser on the Wii, despite it being handicapped in terms of resolution. You can scroll pages no problem, as long as the width is reasonable. Pages are getting better at scaling anyway.
Anyway, I am starting to ramble, because I have to get into bed. This has prompted me to test my PSPs browser a bit more by the way, and so far it passes almost every CSS1 test with flying colors. Sure, that's not the latest tech, but still not bad.