I think its due to that side the Passengers come off, the jetty goes on that side and or stairs. So they shut Engine one off first.
In what sense would it cause stress to an already strong airframe, its normal I think for them to shut the engines down so quick. I noticed a BA A320 at EGLL T5 the other week, both engines and Beacon were off as soon as he applied the parking brake. I'm not an expert. Someone else will be able to clarify.
But I am pretty sure its so nobody putting the jetty or stairs near the door aft of the cockpit, is so they don't get sucked in. There more likely to go left side first than right so they passengers can disembark.
Regards,
R..