It's all crazy talk, I have been going to spas in Chinatown or close by in Center City for almost 7 years and to date I never had any problems, including no parking tickets. Granted, parking in the city can be really tough, but you learn where potential free parking may be possible or find a space on the street with a pay Kiosk. Otherwise parking is only a maximum of $20 for 2 hours in a garage especially on weekends. Osaka/Apple Pie Spa on 16th and Chestnut was the worse for me. I had a provider that I saw a lot several years ago, I would park on Bainbridge below South and walk 6 or more blocks but parking had no time limit. Otherwise the garage nearby the spa charged me $37 if I went over 2 hours when lunch at the spa took too long. But learning the ropes and being creative and not lazy is the key to city parking. I would rather give the girl a little extra tip than to pay for parking.
As for safety and damages to my car, the burbs have been the worse for me. On time before Christmas all my gifts for a couple providers were stolen out of my trunk in the parking lot at my office in Plymouth Meeting. Three times I have been rear ended, and once I rear ended someone in the burbs. I have many fewer problems in the city where I also have lived in for over forty years. I am only counting my problems in the burbs for my 7 year mongering the period.
So I think it's more than worth any trouble you may encounter in the city because the quality and choice to of good places far exceeds what is available in the burbs.