Wild World is still playable, and many people, myself included, do still play it. However, there are several reasons why maybe it's not as talked about as other games such as New Leaf.
Firstly it's a very old game and since it's release back in 2005 another two main games and two (soon to be three) spin off games have been released. Players tend to focus on the newer games and somewhat forget about Wild World.
Secondly, many people contest that Wild World is actually the weakest main game released. Whilst it saw the new addition of visiting other players towns, the game dropped a hell of a lot of content that we're only just starting to see make a return in the main games. Holidays like Christmas and Halloween were dropped, along with multi layer towns. There also wasn't a huge amount in the way of customising the town, and whilst it can be argued that Animal Crossing GameCube didn't have this either, the original version had a lot more events and content.
For all it's flaws, Wild World did introduce visiting another players town either over the Internet or via DS to DS. This was the main attraction for many players as we hadn't seen this feature before! However, in 2014 Nintendo terminated the online function for the DS and Wii. This meant that Wild World players could no longer visits each other town across the internet. Whilst players can still visit each other using the DS to DS method, this require the two players to be next to each other.
The wifi turn off meant that there was even less content in a game that already struggled. Many people didn't see the point in playing when newer and better games came out.
So whilst there are still people who play it every now and then, the internet function is pretty useless, which means certain things in the game can be achieved (the upgrade for Tom Nooks store for example). You cannot get friend codes or visit other people's town across the wifi.
Leave nothing but footprints, take nothing but memories...
Playing Wild World online is definitely possible, but you need to do some finicky hacks of which I don't have a DS to do, definitely going to get an old broken DS and fix it up just to try and hack it JUST FOR multiplayer.
Edit: Oh my lord apparently you can do it on the 3DS too. Unfortunately one of my loving amazing siblings decided to rip the circle pad off my 3DS.