I don’t know why people keep making this mistake. The body of Shimano rear derailleurs – the front and back plates that make up the parallelogram – have no difference between the short and mid cage road derailleurs - the only difference is the distance between the pulley centres. Shimano tech docs list short and mid cage derailleurs as having the same max cog limit, so if a short cage derailleur on a particular bike doesn’t work with a particular size large cog, the mid cage derailleur will also not work.

Where a mid cage derailleur might help is if you change to a wide spread cassette and the derailleur lacks sufficient capacity for chain take-up… like, for instance, a 50/34 compact crank with a 11/32 cassette needs a RD capacity of 37 teeth, short cage Ultegra has capacity of 33 teeth, mid cage Ultegra has capacity of 39 teeth, but both have listed max cog of 28 teeth... so if you are lucky and the upper pulley of the short length cage RD does not rub on the biggest cogs, the mid cage will also not rub on the biggest cogs. But if the short cage is rubbing on the biggest cog, switching to a mid cage will not help.