I started in Jujutsu and TDK which was bear foot, but I have been wearing shoes training Chinese martial arts for over 20 years and all of that time has been in street clothes or sweats. I will admit when I started with my first shifu I expected to have to take my shoes off, but since he held the first class in the parking lot next to his school I was pretty happy we kept out shoes on. And when we moved inside, since he never had anyone remove thier shoes, I was pretty happy to keep them on there too.
And since I have trained in all sorts of weather on just about every terrain I have been rather happy wearing shoes. A year ago winter I was doing bagua circle walking in my garage and it was well below freezing out side so I am good with shoes, boots, sneakers, dress shoes, just about any foot wear. Use to train Police/military Sanda with my shifu at lunch during work and outside on concrete and even once during a thunderstorm.
Also, doing bagua circle walking, in sneakers, on a carpet, can take a lot of concentration too. My last Bagua Shifu school was carpeted.
I also do a little yoga, but that is in bare feet...just never in my garage in the winter .
I practice in my wife's yoga studio and outside on the beach - but because of shoes you definitely have more options and versatility in your practice - I guess deep down, it's more about personal expression and feel than anything else.