Have to disagree on this. Depending on what is the goal, a 3DS – especially the new type consoles – would be able to handle it. Probably slow, but basic browsing (possibly in mobile mode if a site supports one) should be in range. Adblocking, script blocking and prevention of automatic inclusion for third-party content should be part of such a hypothetical browser to not exhaust all resources in the first second.
In my opinion the problem preventing serious attempts by talented/knowledgeable developers to port a browser engine to 3DS is the "Use your phone! Don't you have a phone?"-attitude. As if the existence of more suitable devices for a task would be a good reason for not trying anything on older stuff.
While we are at it: A powerful PC and a smartphone from the top class could replace pretty much every old thing via emulation.