Historically this was done to save memory but i can't see that that is a good argument here since in order to get AGS to draw the tiles quickly the best way to do it is to cache the map to an object and move the object around to simulate camera movement. So since the whole map is cached anyway we dont save any memory.
There aren't a huge list of advantages to using tiles now that memory constraints are pretty much a thing of the past, but here are some points to consider:
1. By constructing a tile engine you can also define collision areas right into the tile properties, so when a player interacts with them the logic to block/slow/allow them to pass or whatever is there without the need for drawing walkable areas over the background and blocking out trees, fences, etc.
2. Similar to the above, but with a tile engine you can also define DRAW ORDER so you can automatically make some things appear in front of the player and some things behind without the need for drawing walk behinds. This is provided that you allow tile layering so more than one image can occupy the same space.
3. You can avoid using regions by specifying a 'region tile' and then drawing it on the top layer of your tiled background.
4. Tilesets make it much easier to construct/edit backgrounds.
5. A tile editor would make expanding the game trivial from an artistic standpoint or making a sequel using the same assets, etc.
6. Can produce a variety of backgrounds rapidly with even a modest tileset, which is particularly useful if you hate designing backgrounds or are on a time limit.
Also, if you don't want to bother with making an engine but want some of the benefits of tiles, some art programs will allow you to draw with tiles and then save the complete background. You'll have to do the regions and walkbehinds manually but it's a step between all or nothing.