Gosh, I'm inadvertently trendy!
I wear trainers rather like that, they're made by Hoka One One and are the most cushioned running shoe I've come across. They were the talk of the running community as the Next Big Thing a year or two ago, but that rather fell by the wayside.
But I love the cushioning. I've run personal bests at 5k, 10k and Half Marathon.
I don't wear them other than when running (or occasionally when going to/from and event where I don't want to use the bag drop).
They are a serious running trainer - but half the price of these 'fashion' ones. Various