What happens if you ignore the spacing recommendations on the box of ceramic tile?

There is always some expansion in building materials -- even if the tile itself does not expand, the wooden baseboard and house framing will do so with changes in temperature and humidity. This is why you always leave a gap around the edge of any kind of flooring in a room where it meets the walls. It is usually recommended to use a flexible silicone caulk in that space rather than the grout used over the rest of the floor to ensure that perimeter stays fluid.

The large tiles are the larger the recommended grout line to make it look more proportioned. i agree that 3/8" does seem a little large but if these are tiles made to look like rough stone it might be the best option. I had 12" x 12" porcelain tiles installed in my kitchen and they used a 1/4" line with sanded grout and it looks fine but these are much smaller than your tiles. If your tiles have a tapered edge the wider grout line would be suitable -- if the tiles are straight-cut edged, a narrower line is recommended like 1/8" or 1/4", usually with un-sanded grout. i would pay attention to what the manufacturer suggests. And definitely don't butt the tiles directly to the wall -- that is asking for trouble.

thats a large spacing ..much bigger than i have seen used in the uk ..im a builder ..here we would use a 3mm spacer ...there are 25mm to the inch ..on floors where you need a bigger spacing we would use 5mm spacers ...any more will look silly ..go for 1/4"