Like the question states, is there any reason why I should open a chest from arena X over a chest from arena X+1? The chest from the higher arena will give you more cards and coins than the lower arena.
As far as I can tell, no.
The only reason to open the Arena X chests would be that you're out of Arena X+1 chests. Maybe if the higher chest is a gold one and you're saving it for the night or work day.
You many want to clear them out of the way at some point to make room for better ones, but if you're constantly getting just as many chests as you need, I'd postpone opening the lower level ones.
Of coures, they are in your inventory. I'll propably open them at some point anyways. Maybe that time you fall to the lower Arena. Maybe that one day you just don't feel like playing.
I'll have to go the other way though. Yes you should open arena 3 chests if you are n arena 4. You need to precious room for Arena 4 chests. I've lost more than one Arena 4 and then get demoted to 3 because I was full ... Moreover I've found that I need 4 slots to fully make sure I'm always opening a chest and playing for crowns in the allocated 24h, while making sure I don't play games when I'm full. Please check my other answers as to why this is important.